
PublicationsBooks[B3] Geometric Theory of Generalized Functionswith Applications to General Relativity with M. Grosser, M. Oberguggenberger and R. Steinbauer Mathematics and its Applications 537, Kluwer, 2001. [B2] On the Foundations of Nonlinear Generalized Functions I, II. with E. Farkas, M. Grosser and R. Steinbauer Retrieve: math.FA/9912214 [abs, src, pdf, other] and math.FA/9912215 [abs, src, pdf, other] Mem. Amer. Math. Soc. 153, No. 729, 2001. [B1] Barrelledness, Bairelike and (LF)Spaces , Pitman Research Notes in Mathematics Vol. 298, Longman, Harlow 1993, Review in Bull. AMS 32 (3) (1995), 354357 . Preprints[Pre2] Null distance and convergence of Lorentzian length spaceswith R. Steinbauer Subjclass: Metric Geometry (math.MG); General Relativity and Quantum Cosmology (grqc); Mathematical Physics (mathph); Differential Geometry (math.DG) MSCclass: 53C23, 53C50, 53B30, 51K10, 53C80 Retrieve: 2106.05393 [Pre1] A Grothendieck topos of generalized functions I: basic theory with P. Giordano and H. Vernaeve Subjclass: Functional Analysis (math.FA) MSCclass: 46XX, 46Fxx, 30Gxx, 46Txx, 46F30, 26E30, 58A03 Retrieve: 2101.04492 Publications in refereed Journals[J53] Generalized cones as Lorentzian length spaces: Causality, curvature, and singularity theoremswith S. Alexander, M. Graf, and C. Sämann Subjclass: Metric Geometry (math.MG); General Relativity and Quantum Cosmology (grqc); Mathematical Physics (mathph); Differential Geometry (math.DG) MSCclass: 51K10, 53C23, 53C50, 53B30, 53C80 Retrieve: 1909.09575 Journal: Comm. Anal. Geom., to appear. [J52] Parameterdependent linear ordinary differential equations and topology of domains with Vyacheslav M. Boyko and Roman O. Popovych Subjclass: Classical Analysis and ODEs MSCclass: 34A30, 35D30 Retrieve: 1901.02059 Journal: J. Differential Equations 284 (2021), 546575. [J51] A vanishing dynamic capillarity limit equation with discontinuous flux with M. Graf, D. Mitrovic, and D. Vujadinovic Subjclass: Analysis of PDEs MSCclass: 35K65, 42B37, 76S99 Retrieve: 1805.02723 Journal: ZAMP 71, Article number 201 (2020), Article (open access). [J50] The future is not always open with James D.E. Grant, Clemens Sämann, and Roland Steinbauer Subjclass: Differential Geometry (math.DG); General Relativity and Quantum Cosmology (grqc); Mathematical Physics (mathph) MSCclass: 53C50, 83C75 Retrieve: 1901.07996 Journal: Letters in Math. Phys. 110 (2020), no. 1, 83103. [J49] Laplace transformation of vectorvalued distributions and applications to CauchyDirichlet problems with E. Nigsch and N. Ortner Subjclass: Analysis of PDEs MSCclass: 44A10, 35E05, 35E15, 35C05, 35J30, 35J40, 35L35 Retrieve: 1809.10444 Journal: J. Math. Anal. Appl. 478, 9901004, 2019. [J48] Inextendibility of spacetimes and Lorentzian length spaces with J.D.E. Grant and C. Sämann Subjclass: Differential Geometry, Metric Geometry, General Relativity and Quantum Cosmology MSCclass: 53C23, 53C50, 53B30, 53C80, 83C75 Retrieve: 1804.10423 Journal: Ann. Global Anal. Geom. 55:133147 (2019). [J47] Lorentzian length spaces with C. Sämann Subjclass: Differential Geometry, Metric Geometry, General Relativity and Quantum Cosmology MSCclass: 53C23, 53C50, 53B30, 53C80 Retrieve: 1711.08990 Journal: Ann. Global Anal. Geom. 54, no. 3, 399447 (2018). [J46] The HawkingPenrose singularity theorem for $C^{1,1}$Lorentzian metrics with M. Graf, J. D. E. Grant, and R. Steinbauer Subjclass: General Relativity and Quantum Cosmology, Differential Geometry MSCclass: 83C75, 53B30 Retrieve: 1706.08426 Journal: Comm. Math. Phys., 360 (2018), no. 3, 10091042. [J45] Wellposedness theory for degenerate parabolic equations on Riemannian manifolds with M. Graf and D. Mitrovic Subjclass: Analysis of PDE MSCclass:35K65, 42B37, 76S99 Retrieve: 1612.08195 Journal: J. Differential Equations 263, no. 8, 47874825 (2017). [J44] Singular reduction modules of differential equations with V.M. Boyko and R. Popovych Subjclass: Mathematical Physics, Symmetry Analysis MSCclass: 35A30, 35C05, 35K55, 35K55, 35L70 Retrieve: 1201.3223 Journal: J. Math. Phys. 57, 101503 (2016) [J43] A convenient notion of compact set for generalized functions with P. Giordano Subjclass: Functional Analysis MSCclass:46F30, 46A13, 13J99 Retrieve: 1411.7292 Journal: Proc. Edinburgh Math. Soc. (2) 61 (2018), no. 1, 5792. [J42] The Penrose singularity theorem in regularity $C^{1,1}$ with R. Steinbauer and J. A. Vickers Subjclass: General Relativity and Quantum Cosmology, Differential Geometry MSCclass: 83C75, 53B30 Retrieve: 1502.00287 Journal: Class. Quant. Grav., 32 (2015), no. 15, 155010, 12 pp. This article was featured among the Highlights of 20142015 in Mathematical Relativity by the Editorial Board of Classical and Quantum Gravity. [J41] Hawking's singularity theorem for $C^{1,1}$metrics with R. Steinbauer, M. Stojkovic, and J. A. Vickers Subjclass: General Relativity and Quantum Cosmology, Differential Geometry MSCclass: 83C75, 53B30 Retrieve: 1411.4689 Journal: Class. Quant. Grav., 32 (2015), no. 7, 075012, 19 pp. This article was featured among the Highlights of 20142015 in Mathematical Relativity by the Editorial Board of Classical and Quantum Gravity. [J40] Strongly internal sets and generalized smooth functions with P. Giordano and H. Vernaeve Subjclass: Functional Analysis MSCclass:46F30, 03H05, 46S20 Retrieve: 1402.3534 Journal: J. Math. Anal. Appl., 422 (2015), no. 1, 5671. [J39] A regularisation approach to causality theory for $C^{1,1}$Lorentzian metrics with R. Steinbauer, M. Stojkovic, and J. A. Vickers Subjclass: Differential Geometry MSCclass:53B30 Retrieve: 1310.4404 Journal: Gen. Relativ. Gravit. (2014) 46:1738. [J38] The exponential map of a $C^{1,1}$metric with R. Steinbauer and M. Stojkovic Subjclass: Differential Geometry MSCclass:53B20, 53B21, 53B30 Retrieve: 1306.4776 Journal: Differential Geom. Appl. 34, 1424, 2014. [J37] Symplectic modules over Colombeaugeneralized numbers with G. Hörmann and S. Konjik Subjclass: Rings and Algebras, Linear Algebra MSCclass: 15A63, 15A18, 15A21, 46F30 Retrieve: 1211.2629 Journal: Comm. Algebra 42: 33583577, 2014. [J36] Singularity structures for noncommutative spaces with S. Dave Subjclass: Global Analysis MSCclass: 58J40, 58J47, 58J42 Retrieve: 1111.6570 Journal: Trans. Amer. Math. Soc., 367, no. 1, 251273, 2015. [J35] Optimal regularization processes on complete Riemannian manifolds with S. Dave and G. Hörmann Subjclass: Functional Analysis, Global Analysis MSCclass: 58J37,46F30,46T30,35A27,35L05 Retrieve: 1003.3341 Journal: Tokyo J. Math., Vol. 36, No. 1, 2013. [J34] New topologies on Colombeau generalized numbers and the FermatReyes theorem with P. Giordano Subjclass: Functional Analysis, Algebras of Generalized Functions MSCclass: 46F30, 46T20 Retrieve: 1201.3887 Journal: J. Math. Anal. Appl., 399 (2013), no. 1, 229�238. [J33] A global theory of algebras of generalized functions II: tensor distributions with M. Grosser, R. Steinbauer, and J. Vickers Subjclass: Functional Analysis, Global Analysis MSCclass: 46F30; 46T30, 26E15, 58B10, 46A17 Retrieve: 0902.1865 Journal: New York J. Math. 18 (2012) 139199. [J32] Manifoldvalued generalized functions in full Colombeau spaces with E. Nigsch Subjclass: Functional Analysis MSCclass: 46F30,46T30,26E15 Retrieve: 1103.5845 Journal: Comm. Math. Univ. Carolinae 52 (4) (2011) 519534. [J31] Topological and algebraic structures on the ring of Fermat reals with Paolo Giordano Subjclass: Commutative Algebra MSCclass: 03H05, 12D, 13J25 Retrieve: 1104.1492 Journal: Israel J. Math., 193 (2013), no. 1, 459�505. [J30] Algebras of generalized functions with smooth parameter dependence with A. Burtscher Subjclass: Functional Analysis, Algebra MSCclass: 46F30,13J25,46T30 Retrieve: 1010.5752 Journal: Proc. Edinburgh Math. Soc. (Series 2), Vol. 55, Issue 01, pp 105  124, 2012. [J29] Generalized conditional symmetries of evolution equations with R. Popovych Subjclass: Mathematical Physics, Analysis of PDE MSCclass: 35B06, 35K55, 35K57, 35C05 Retrieve: 1011.0277 Journal: J. Math. Anal. Appl. 379 No. 1, 444460, 2011. [J28] Singular reduction operators in two dimensions. with R. Popovych Subjclass: Symmetry group analysis of PDEs; Mathematical Physics MSCclass: 35A30, 35C05, 35K55, 35K55, 35L70 Retrieve: 0808.3577 Journal: J. Phys. A: Math. Theor. 41 (2008) 505201. [J27] Admissible transformations of nonlinear Schrödinger equations. with R. Popovych and H. Eshragi Subjclass: Symmetry group analysis of PDEs; Mathematical Physics MSCclass: 35A30; 35Q55;58J70;35C05 Retrieve: mathph/0611061 [abs, src, pdf, other] Journal: Acta. Appl. Math. 109, 315359 (2010). [J26] Potential Conservation Laws. with R. Popovych Subjclass: Symmetry group analysis of PDEs; Mathematical Physics MSCclass: 35A99; 35A30; 35K57; 35K05 Retrieve: 0803.1156 Journal: J. Math. Phys. 49, 103506 (2008) (34 pages). [J25] Foundations of the calculus of variations in generalized function algebras. with S. Konjik and M. Oberguggenberger Subjclass: Functional Analysis, Global Analysis MSCclass: 49J27, 46F30, 49K27, 37K05 Retrieve: 0707.1842 [abs, pdf, other] Journal: Acta Appl. Math. 103: 169199, 2008. [J24] Conservation Laws and Potential Symmetries of Linear Parabolic Equations. with R. Popovych and N. Ivanova Subjclass: Symmetry group analysis of PDEs; Mathematical Physics MSCclass: 35A30; 35Q55;58J70;35C05 Retrieve: 0706.0443 [abs, pdf, other] Journal: Acta Appl. Math., 100, Number 2, 113185, 2008. [J23] Sheaves of nonlinear generalized functions and manifoldvalued distributions. with R. Steinbauer and J. Vickers Subjclass: Functional Analysis, Differential Geometry. MSCclass: 46F30, 53B20, 46T30 Retrieve: math.FA/0609358 [abs, src, pdf, other] Journal: Trans. Amer. Math. Soc. 361, 51775192, 2009. [J22] Generalized solutions of the VlasovPoisson system with singular data. with I. Kmit, R. Steinbauer Subjclass: Analysis of PDEs; Mathematical Physics MSCclass: 35A05; 46F30, 35Q72, 82C22 Retrieve: math.AP/0601552 [abs, src, pdf, other] Journal: J. Math. Anal. Appl., 340, No. 1, 575587, 2008. [J21] Generalized Group Actions in a Global Setting. with S. Konjik Subjclass: Functional Analysis, Differential Geometry MSCclass: 46F30; 58D19 Retrieve: math.DG/0412045 [abs, src, pdf, other] Journal: J. Math. Anal. Appl., 322, 420436, 2006. [J20] Group invariants in algebras of generalized functions. with S. Konjik Subjclass: Functional Analysis, Differential Geometry MSCclass: 46F30; 58D19; 46T30; 35A30 Retrieve: math.DG/0412045 [abs, src, pdf, other] Journal: Integral Transforms Spec. Funct., 17, No.23, 7784, 2006. [J19] Global Gronwall Estimates for Integral Curves on Riemannian Manifolds. with H. Schichl, R. Steinbauer and J. A. Vickers Subjclass: Differential Geometry MSCclass: 53B21; 53C22; 34A26 Retrieve: math.DG/0412045 [abs, src, pdf, other] Journal: Rev. Mat. Complut., no. 1, 133137, 2006. [J18] On Local Solutions of the Relativistic VlasovKleinGordon system. with G. Rein, R. Steinbauer and G. Teschl Subjclass: Partial Differential Equations MSCclass: 35A07; 35Q72; 35Q40; 82C22 Retrieve: math.AP/0407028 [abs, src, pdf, other] Journal: Electron. J. Diff. Eqns., Vol. 2005, No. 01, 117, 2005. [J17] Generalized connections and curvature. with R. Steinbauer and J. Vickers Subjclass: Functional Analysis, Differential Geometry, Mathematical Physics. MSCclass: 46F30, 53B05, 46T30 Retrieve: math.FA/0403040 [abs, src, pdf, other] Journal: Math. Proc. Cambridge Philos. Soc., 139, no. 3, 497521, 2005. [J16] Nonsmooth differential geometry and algebras of generalized functions. Subjclass: Functional Analysis, Global Analysis. MSCclass: 46F30, 53B20, 46T30 Retrieve: math.FA/0312487 [abs, src, pdf, other] Journal: J. Math. Anal. Appl. 297, 456471, 2004. [J15] Generalized flows and singular ODEs on differentiable manifolds. with M. Oberguggenberger, R. Steinbauer and J. Vickers Subjclass: Functional Analysis, Global Analysis. MSCclass: 46F30, 53B20, 46T30 Retrieve: math.FA/0304131 [abs, src, pdf, other] Journal: Acta Appl. Math. 80, 221241, 2004. [J14] Global weak solutions of the relativistic VlasovKleinGordon System. with G. Rein, R. Steinbauer and G. Teschl Subjclass: Partial Differential Equations MSCclass: 35D05, 35Q72 Retrieve: math.AP/0209303 [abs, src, pdf, other] Journal: Comm. Math. Phys. 238 (12), 367378, 2003. [J13] Intrinsic characterization of manifoldvalued generalized functions. with R. Steinbauer and J. Vickers Subjclass: Functional Analysis, Global Analysis. MSCclass: 46F30, 53B20, 46T30 Retrieve: math.FA/0205223 [abs, src, pdf, other] Journal: Proc. London Math. Soc., 87 (2), 451470, 2003. [J12] Generalized pseudoRiemannian Geometry. with R. Steinbauer Subjclass: Functional Analysis, Mathematical Physics. MSCclass: 46F30, 46T30 Retrieve: math.FA/0107057 [abs, src, pdf, other] Journal: Trans. Amer. Math. Soc. 354, no. 10, 41794199, 2002. [J11] Generalized functions valued in a smooth manifold. Subjclass: Functional Analysis, Global Analysis. MSCclass: 46F30, 53B20, 46T30 Retrieve: math.FA/0107051 [abs, src, pdf, other] Journal: Monatsh. Math., 137, 3149, 2002. [J10] Symmetry group analysis of weak solutions. with N. Dapic and S. Pilipovic Subjclass: Differential Equations, Lie Group Actions, Generalized Functions MSCclass: 46F30; 58D19 Retrieve: math.FA/0104055 [abs, src, pdf, other] Journal: Proc. London Math. Soc. 84 (3), 686710, 2002. [J9] Foundations of a nonlinear distributional geometry. with R. Steinbauer Subjclass: Functional Analysis, Mathematical Physics. MSCclass: 46F30;46T30;46F10;37J05 Retrieve: math.FA/0102019 [abs, src, pdf, other] Journal: Acta Appl. Math. 71, 179206, 2002. [J8] A Global Theory of Algebras of Generalized Functions. with M. Grosser, R. Steinbauer and J. Vickers Subjclass: Functional Analysis; Mathematical Physics MSCclass: 46F30; 46T30 Report: ESIPreprint 813 Retrieve: math.FA/9912216 [abs, src, pdf, other] Journal: Advances in Math. 166, No. 1, 5072, 2002 . [J7] Microlocal properties of basic operations in Colombeau algebras. with G. Hörmann Subjclass: Functional Analysis MSCclass: 46F30; 35A21 Retrieve: math.FA/0008206 [abs, src, pdf, other] Journal: J. Math. Anal. Appl. 261, 254270, 2001. [J6] Group Analysis of Differential Equations and Generalized Functions with M. Oberguggenberger Subjclass: Functional Analysis; Analysis of PDEs MSCclass: 46F30; 35Dxx; 35A30; 58G35 Report: math.FA/9912217 [abs, src, pdf, other] Journal: SIAM J. Math. Anal. 31 (2000) no. 6, 11921213. [J5] Regularized derivatives in a 2dimensional model of selfinteracting fields with singular data with G. Hörmann Subjclass: Analysis of PDEs; Functional Analysis MSCclass: 35Dxx; 46F10; 35Lxx; 78A25 Retrieve: math.FA/9912219 [abs, src, pdf, other] Journal: Zeitschr. Anal. u. Anw. 19, Nr 1 (2000), 147158 [J4] A note on the Penrose junction conditions. with R. Steinbauer Subjclass: General Relativity and Quantum Cosmology; Mathematical Physics MSCclass: 83Cxx; 46F10; 83C35; 35Dxx Journalref: Class. Quant. Grav. 16 (1999) 12551264 Report: ESIPreprint 627. Retrieve: grqc/9811007 [abs, src, pdf, other] Journal: Classical and Quantum Gravity 16 (1999), 12551264, This article was featured among the highlights of 1999 and 2000 in Classical and Quantum Gravity. [J3] A rigorous solution concept for geodesic and geodesic deviation equations in impulsive wave geometries. with R. Steinbauer Subjclass: General Relativity and Quantum Cosmology; Mathematical Physics MSCclass: 83C35; 83C99; 46F10; 35Dxx Report: ESIPreprint 558. Retrieve: grqc/9806009 [abs, src, pdf, other] Journal: Journal of Mathematical Physics Vol. 40, Nr 3 (1999), 1479  1489. [J2] Characterization of Colombeau Generalized Functions by their Pointvalues with M. Oberguggenberger Subjclass: Functional Analysis; MSCclass: 46F10; 03H05; 35Dxx Retrieve: point values Journal: Math. Nachr. 203 (1999), 147157. [J1] Nonlinearity and SelfInteraction in Physical Field Theories with Singularities with G. Hörmann Subjclass: Functional Analysis;Analysis of PDEs. MSCclass: 35Dxx, 46F10,35Qxx,78A25,35Q60. Journal: Integral Transf. Special Funct., Vol. 6, No.14 (1997), 190199. Contributions to Proceedings[P10] Inverse Function Theorems for Generalized Smooth Functionswith P. Giordano Subjclass: Functional Analysis MSCclass:46F30, 26E30 Retrieve: 1602.00013 In: M. Oberguggenberger, J. Toft, J. Vindas, P. Wahlberg, Generalized Functions and Fourier Analysis, Springer, 2017, pp 95  114. [P9] A regularization approach to nonsmooth symplectic geometry with G. Hörmann and S. Konjik Subjclass: Differential Geometry MSCclass: 53D05, 46F30 Retrieve: 1403.0234 Journal: Operator Theory: Advances and Applications, Birkäuser, Basel, to appear. [P8] Geometric regularization on Riemannian and Lorentzian manifolds with S. Dave and G. Hörmann Subjclass: Global Analysis MSCclass: 58J40, 58J47, 58J42 Retrieve: 1107.0010 Journal: M. Ruzhansky, J. Wirth (Eds.) Evolution Equations of Hyperbolic and Schrödinger Type, Progress in Mathematics 301, Birkäuser, 87102, 2012. [P7] Wave equations on nonsmooth spacetimes with G. Hörmann and R. Steinbauer Subjclass: Analyis of PDEs MSCclass: 58J45, 35L05, 35L15, 35D99, 46F30 Retrieve: 1107.0014 Journal: M. Ruzhansky, J. Wirth (Eds.) Evolution Equations of Hyperbolic and Schrödinger Type, Progress in Mathematics 301, Birkäuser, 163186, 2012. [P6] Is a nonclassical symmetry a symmetry? with R. Popovych Subjclass: Symmetry group analysis of PDEs; Mathematical Physics MSCclass: 35A30, 35C05 Retrieve: 0903.0821 Journal: Proceedings of 4th Workshop "Group Analysis of Differential Equations and Integrable Systems" (2630 October 2008, Protaras, Cyprus), 2009, 107120 [P5] Recent progress in special Colombeau algebras: geometry, topology, and algebra Subjclass: Functional Analysis, Differential Geometry, Algebra MSCclass: 46F30, 46T30, 46A20, 16D25, 53B20 Retrieve: 0712.4340 Journal: Banach Center Publications 88, 175184, 2010. [P4] Diffeomorphism invariant Colombeau algebras. Part III: Global theory. Subjclass: Functional Analysis; Mathematical Physics MSCclass: 46F30; 46T30 Retrieve: math.FA/0104272 [abs, src, pdf, other] in: Nonlinear Algebraic Analysis and Applications, Proceedings of the International Conference on Generalized Functions (ICGF 2000), edited by A. Delcroix, M. Hasler, J.A. Marti and V. Valmorin, Cottenham, Cambridge, Cambridge Scientific Publishers 117126, 2004. [P3] Diffeomorphism invariant construction of nonlinear generalized functions with M. Grosser, R. Steinbauer, H. Urbantke, and J. Vickers, Ann. Phys. 9 Spec. Issue, SI173SI174. [P2] Lie Symmetries of Differential Equations in a Generalized Functions Setting. in: M. Grosser, G. Hörmann, M. Kunzinger, M. Oberguggenberger (Eds.), Nonlinear Theory of Generalized Functions, CRC Research Notes in Mathematics 401, 241250, (1999). [P1] Symmetries of Differential Equations in Colombeau Algebras. with M. Oberguggenberger in: N. H. Ibragimov, F. M. Mahomed (Eds.), Modern Group Analysis VI, New Age Int. Publ., 920, (1997). Editorial Activities[E3] NonRegular Spacetime Geometrywith P. Chrusciel, J.D.E. Grant and E. Minguzzi Proceedings of the eponymous conference, June 2022, 2017, Florence Journal of Physics: Conference Series, Volume 968, conference 1 [E2] Topics in Partial Differential Equations, Harmonic Analysis, and Geometry with M. Grosser, S. Pilipovic and R. Steinbauer Proceedings of the International Conference on Generalized Functions GF2009, Vienna, August 31September 4, 2009 Integral Transforms Spec. Funct. 22 (2011), no. 45. [E1] Nonlinear Theory of Generalized Functions. with M. Grosser, G. Hörmann and M. Oberguggenberger Proceedings of a Workshop held at ESI, Oct.Dec. 1997, CRC Research Notes in Mathematics 401 (1999). ISBN 0849306493. Last modified June 16, 2021 by Michael Kunzinger. 