Home Page of Roland Steinbauer




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Scientific Publications

Monographs

[M2] Geometric Theory of Generalized Functions (with Applications to General Relativity)
(This item received a Featured Review by the AMS)
Authors: Michael Grosser, Michael Kunzinger, Michael Oberguggenberger, Roland Steinbauer
MSC-class: 46F30; 35A30, 35Q75, 46-02, 46T30, 58-02, 83C99
Ref: Mathematics and its Applications, Vol. 537, Kluwer, Dodrecht, 2001.

[M1] On the foundations of nonlinear generalized functions I,II
(This item received a Featured Review by the AMS)
Authors: Eva Farkas, Michael Grosser, Michael Kunzinger, Roland Steinbauer
MSC-class: 46F30, 26E15, 46E50, 35D05
Ref: Mem. Amer. Math. Soc. 729, 153, 2001.
ArXive: math.FA/9912214

Textbook

[T1'] Einführung in das mathematische Arbeiten
(German; Introduction to working mathematically.)

Authors: Hermann Schichl, Roland Steinbauer
MSC-Class: 00A35; 00A05, 00-01
Ref: 2nd, revised Edition, Springer, Heidelberg, 2012.

[T1] Einführung in das mathematische Arbeiten
(German; Introduction to working mathematically.)

Authors: Hermann Schichl, Roland Steinbauer
MSC-Class: 00A35; 00A05, 00-01
Ref: Springer, Heidelberg, 2009.

Preprints

[Pre1] On geodesics in low regularity
Authors: Clemens Sämann, Roland Steinbauer
MSC-class: 53B30, 53C22, 34A36, 83C99
ArXive: arXiv:1710.10887 [math-ph]


Peer-reviewed Research Articles

[P46] The Hawking-Penrose singularity theorem for $C^{1,1}$-Lorentzian metrics
Authors: Melanie Graf, James Grant, Michael Kunzinger, Roland Steinbauer
MSC-class: 83C75, 53B30
Ref: Commun. Math. Phys. online first, 34pp, (2017)
ArXive:
arXiv:1706.08426 [math-ph]

[P45] Geodesics in nonexpanding impulsive gravitational waves with $\Lambda$, part II
(Featured as Editor's pick in Journal of Mathematical Physics)
Authors: Clemens Sämann, Roland Steinbauer
MSC-class: 83C15, 83C35, 46F10, 34A36
Ref: J. Math. Phys. 58(11), 112503, 18, (2017)
ArXive: arXiv:1704.05383

[P44] Penrose junction conditions extended: impulsive waves with gyratons
Authors: Jiri Podolsky, Robert Svarc, Roland Steinbauer, Clemens Sämann
MSC-class: 83C15, 83C35, 83C10
Ref: Phys. Rev. D 96 064043, 11 (2017)
ArXive: arXiv:1704.08570

[P43] Completeness of general pp-wave spacetimes and their impulsive limit
Authors: Clemens Sämann, Roland Steinbauer, Robert Svarc
MSC-class: 83C15, 83C35, 83C10, 34A36
Ref: Class. Quantum Grav. 33(21) 215006, 27 (2016)
ArXive: arXiv:1607.01934

[P42] The global uniqueness and $C^1$-regularity of geodesics in expanding impulsive gravitational waves
Authors: Jiri Podolsky, Clemens Sämann, Roland Steinbauer, Robert Svarc
MSC-class: 83C15, 83C35, 46F10, 34A36
Ref: Class. Quantum Grav. 33(19) 195010, 23 (2016)
ArXive: arXiv:1602.05020

[P41] Geodesics in nonexpanding impulsive gravitational waves with $\Lambda$, part I
Authors: Clemens Sämann, Roland Steinbauer, Alexander Lecke, Jiri Podolsky
MSC-class: 83C15, 83C35, 46F10, 34A36
Ref: Class. Quantum Grav. 33(11) 115002, 33 (2016)
ArXive: arXiv:1509.04914

[P40] The Penrose singularity theorem in regularity $C^{1,1}$
(Featured as one of the highligths 2015 in Classical and Quantum Gravity)
Authors: Michael Kunzinger, Roland Steinbauer, James A. Vickers
MSC-class: 83C75, 53B30
Ref: Class. Quantum Grav. 32(15) 155010, 12 (2015)
ArXive: arXiv:1502.00287

[P39] Geodesic completeness of generalized space-times
Authors: Clemens Sämann, Roland Steinbauer
MSC-class: 46F30, 83C15, 83C35
Ref: in Pseudo-differential operators and generalized functions.
Pilipovic, S., Toft, J. (eds) Operator Theory: Advances and Applications vol. 245. Birkhäuser/Springer, 243--253, 2015.
ArXive: arXiv:1310.2362

[P38] Hawking's singularity theorem for $C^{1,1}$-metrics
(Featured as one of the highligths 2014/15 in Classical and Quantum Gravity)
Authors: Michael Kunzinger, Roland Steinbauer, Milena Stojkovic, James A. Vickers
MSC-class: 83C75, 53B30
Ref: Class. Quantum Grav. 32(7) 075012, 19 (2015)
ArXive: arXiv:1411.4689

[P37] The global existence, uniqueness and C^1-regularity of geodesics in nonexpanding impulsive gravitational waves
Authors: Jiri Podolsky, Clemens Sämann, Roland Steinbauer, Robert Svarc
MSC-class: 83C15, 34A36, 83C35
Ref: Class. Quantum Grav. 32 025003, 23 (2015)
ArXive: arXiv:1409.1782

[P36] Gyratonic pp-waves and their impulsive limit
Authors: Jiri Podolsky, Roland Steinbauer, Robert Svarc
MSC-class: 83C15, 83C35
Ref: Phys. Rev. D 90, 044050, 15 (2014).
ArXive: arXiv:1406.3227

[P35] A regularisation approach to causality theory for $C^{1,1}$-Lorentzian metrics
Authors: Michael Kunzinger, Roland Steinbauer, James A. Vickers, Milena Stojkovic
MSC-class: 53B30
Ref: Gen. Relativ. Gravit. 46, 1738, 18 (2014).
ArXive: arXiv:1310.4404

[P34] The exponential map of a $C^{1,1}$-metric
Authors: Michael Kunzinger, Roland Steinbauer, Milena Stojkovic
MSC-class: 53B20, 53B21, 53B30
Ref: Differential Geom. Appl. 34, 14-24 (2014).
ArXive: arXiv:1306.4776

[P33] Every Lipschitz metric has $C^1$-geodesics
Author: Roland Steinbauer
MSC-class: 53B30, 34A36
Ref: Class. Quantum Grav. 31 057001 (2014).
ArXive: arXiv:1311.0300

[P32] The regularity of geodesics in impulsive pp-waves
Authors: Alexander Lecke, Roland Steinbauer, Robert Svarc
MSC-class: 83C15, 34A36, 83C35
Status: Gen. Relativ. Gravit. 46 1648 (2014).
ArXive: arXiv:1310.1322

[P31] Wave equations and symmetric first-order systems in case of low regularity
Authors: Clemens Hanel, Günther Hörmann, Christan Spreitzer, Roland Steinbauer
MSC-class: 46F30; 35L45, 35D30, 35Q75
Ref: in Pseudo-differential operators, generalized functions and asymptotics.
Selected papers of the 8th ISAAC congress, Moscow, Russia, August 22–27, 2011.

Molahajloo, S. et al., (eds) Operator Theory: Advances and Applications vol. 231. Birkhäuser/Springer, 283--296, 2013.
ArXive: arXiv:1202.0406

[P30] On the completeness of impulsive gravitational wave spacetimes
Authors:Clemens Sämann, Roland Steinbauer
MSC-class: 83C35, 83C75
Ref: Class. Quantum Grav. 29, 245011 (2012).
ArXive: arXiv:1207.2633

[P29] Wave equations on non-smooth space-times
Authors: Günther Hörmann, Michael Kunzinger, Roland Steinbauer
MSC-class: 46F30; 46T30, 26E15, 58B10, 46A17
Ref: in Asymptotic Properties of Solutions to Hyperbolic Equations, M.~Ruzhansky and J.~Wirth, (eds.)
Progress in Mathematics 301. Birkhäuser, 162--186, (2012).
ArXive: arXiv:1107.0014

[P28] A global theory of algebras of generalized functions II: tensor distributions
Authors: Michael Grosser, Michael Kunzinger, Roland Steinbauer, James Vickers
MSC-class: 58J45; 35L05, 35L15, 35D99, 46F30
Ref: New York J. Math. 18, 139--199, (2012).
ArXive: arXiv:0902.1865

[P27] A geometric approach to full Colombeau algebras
Authors: Roland Steinbauer
MSC-class: 46T30; 46F30
Ref: Banach Center Publ. 88, 267--272 (2010).
ArXive: arXiv:0710.2096

[P26] On the Geroch-Traschen class of metrics
Authors: Roland Steinbauer, James Vickers
MSC-class: 83C75; 46T30, 53B30, 46F10, 46F30
Ref: Class. Quantum Grav. 26, 065001, (2009).
ArXive: arXiv:0811.1376

[P25] The wave equation on singular space times
Authors: James Grant, Eberhard Mayerhofer, Roland Steinbauer
MSC-class: 83C75; 46F30, 35D05, 35Q75
Ref: Commun. Math. Phys. 285(2), 399--420, (2009).
ArXive: arXiv:0710.2007

[P24] Sheaves of nonlinear generalized functions and manifold-valued distributions
Authors: Michael Kunzinger, Roland Steinbauer, James Vickers
MSC-class: 46T30; 46F30, 53B20
Ref: Trans. Amer. Math. Soc. 361, 5177-5192, (2009).
ArXive: math.FA/0609358

[P23] A note on distributional semi-Riemannian geometry
Authors: Roland Steinbauer
MSC-class: 46T30, 53B30, 46F10, 46F30
Ref: Novi Sad J. Math. 38 (3), 189-199 (2008).
ArXive: arXiv:0812.0173

[P22] Generalized solutions of the Vlasov-Poisson system with singular data
Authors: Irina Kmit, Michael Kunzinger, Roland Steinbauer
MSC-class: 35A05; 46F30, 35Q72, 82C22
Ref: J. Math. Anal. Appl. 340, 575-587, (2008).
ArXive: math.AP/0601552

[P21] The use of generalized functions and distributions in general relativity
(Featured as one of the highligths 2005/06 in Classical and Quantum Gravity)
Authors: Roland Steinbauer, James Vickers
MSC-class: 8302
Ref: Class. Quantum Grav. 23(10), R91-R114, (2006).
ArXive: gr-qc/0603078

[P20] Global Gronwall estimates for integral curves on Riemannian manifolds
Authors: Michael Kunzinger, Hermann Schichl, Roland Steinbauer, James Vickers
MSC-class: 53B21, 53C22, 34A26
Ref: Rev. Mat. Complut., 19(1), 133-137, (2006).
ArXive: math.DG/0412045

[P19] On classical solutions of the relativistic Vlasov-Klein-Gordon system
Authors: Michael Kunzinger, Gerhard Rein, Roland Steinbauer, Gerald Teschl
MSC-class: 35A07; 35Q72; 35Q40; 82C22
Ref: EJDE, Vol. 2005(1), 1-17, (2005).
ArXive: math.AP/0407028

[P18] Generalised connections and curvature
Authors: Michael Kunzinger, Roland Steinbauer, James Vickers
MSC-class: 53C05, 53B05, 46T30,46F30, 46F20
Ref: Math. Proc. Cambridge Philos. Soc. 139(3), 497--521, (2005).
ArXive: math.FA/0403040

[P17] Generalized flows and singular ODEs on differentiable manifolds
Authors: Michael Kunzinger, Michael Oberguggenberger, Roland Steinbauer, James Vickers
MSC-class: 46F30, 34G20, 46T30, 53B20
Ref: Acta Appl. Math, 80, 221-241, (2004).
ArXive: math.FA/0304131

[P16] Diffeomorphism invariant Colombeau algebras. Part I: Local theory
Author: Roland Steinbauer
MSC-class: 46F30, 46E50, 35D05, 26E15
Ref: 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 2004, 333-344 (2004).
ArXive: math.FA/0104269

[P15] Nonlinear distributional geometry and general relativity
Authors: Roland Steinbauer
MSC-class: 46F30, 46T30, 46F10, 83C05, 83C35
Ref: 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 2004, 345-356 (2004).
ArXive: math-ph/0104041

[P14] Geodesics in spacetimes with expanding impulsive gravitational waves
Authors: Jiri Podolsky, Roland Steinbauer
MSC-class: 83C15, 83C35
PACS-class: 04.20.Jb, 04.30.Nk
Ref: Phys. Rev. D, 67, 0604013, (2003).
ArXive: gr-qc/0210007

[P13] Global weak solutions of the relativistic Vlasov-Klein-Gordon system
Authors: Michael Kunzinger, Gerhard Rein, Roland Steinbauer, Gerald Teschl
MSC-class: 35D05, 35Q72, 35Q40, 82C22
Ref: Commun. Math. Phys., 238, 367-378 (2003).
ArXive: math.AP/0209303

[P12] Intrinsic characterization of manifold-valued generalized functions
Authors: Michael Kunzinger, Roland Steinbauer, James Vickers
MSC-class: 46T30, 46F30, 53B20
Ref: Proc. London Math. Soc., 87(2), 451-470 (2003).
ArXive: math.FA/0107057

[P11] Generalized pseudo-Riemannian geometry
Authors: Michael Kunzinger, Roland Steinbauer
MSC-class: 46F30, 46T30, 46F10, 83C05
Ref: Trans. Amer. Math. Soc. 354(10), 4179-4199 (2002).
ArXive: math.FA/0107057

[P10] Remarks on the distributional Schwarzschild geometry
Authors: Mark J. Heinzle, Roland Steinbauer
MSC-class: 83C15, 83C15, 83C75, 46F30
Ref: J. Math. Phys. 43(3), 1493-1508 (2002).
ArXive: gr-qc/0112047

[P9] Foundations of a nonlinear distributional geometry
Authors: Michael Kunzinger, Roland Steinbauer
MSC-class: 46F30, 46T30, 46F10, 37J05
Ref: Acta Appl. Math. 71, 179-206, (2002).
ArXive: math.FA/0102019

[P8] A global theory of algebras of generalized functions
Authors: Michael Grosser, Michael Kunzinger, Roland Steinbauer, James Vickers
MSC-class: 46F30, 46T30
Ref: Adv. Math., 166, 50-72 (2002).
ArXive: math.FA/9912216

[P7] Diffeomorphism invariant construction of nonlinear generalized functions
Authors: Michael Grosser, Michael Kunzinger, Roland Steinbauer, Helmuth Urbantke, James Vickers
MSC-class: 46F30, 46T30
Ref: Proceedings of Journees Relativistes 99, Annalen der Physik, Vol 9, Spec. Iss., 173-174 (2000).
Download: here

[P6] On the impulsive limit of gravitational waves
Authors: Roland Steinbauer
MSC-class: 46F30, 83C15, 83C35
Ref: Proceedings of the Spanish Relativity Meeting. ERE-99, 307-311 (2000).
Download: here

[P5] Distributional description of impulsive gravitational waves
Authors: Roland Steinbauer
MSC-class: 46F30, 83C15, 83C35, 46F10
Ref: in Nonlinear Theory of Generalized Functions, edited by Michael Grosser, Günther Hörmann, Michael Kunzinger,
Michael Obergugenberger, (CRC Research Notes, 401, Boca Raton, 1999).
Download: here

[P4] A note on the Penrose junction conditions
(Featured as one of the highligths 1999/2000 in Classical and Quantum Gravity)
Authors: Michael Kunzinger, Roland Steinbauer
MSC-class: 46F30, 83C15, 83C35, 46F10
Ref: Class. Quant. Grav, 16, 1255-1264 (1999).
ArXive: gr-qc/9811007

[P3] A rigorous solution concept for geodesic and geodesic deviation equations in impulsive gravitational waves
Authors: Michael Kunzinger, Roland Steinbauer
MSC-class: 46F30, 83C15, 83C35, 46F10
Ref: J. Math. Phys, 40, 1479-1489 (1999).
ArXive: gr-qc/9806009

[P2] Geodesics and geodesic deviation for impulsive gravitational waves
Authors: Roland Steinbauer
MSC-class: 46F30, 83C15, 83C35, 46F10
Ref: J. Math. Phys. 39, 2201-2212 (1998).
ArXive: gr-qc/9710119

[P1] The ultrarelativistic Reissner-Nordstrom field in the Colombeau algebra
Authors: Roland Steinbauer
MSC-class: 46F30, 83C15, 83C35, 46F10
Ref: J. Math. Phys. 38, 1614-1622 (1997).
ArXive: gr-qc/9606059

Miscellaneous

[Mi4] Ultrarelativistic Black Holes
Author: Roland Steinbauer
Ref: Contribution to the art book YOUBLACKHOLE (Revolver Publishing, Berlin, 2014) by Tomas Eller
Download: here

[Mi3] Large space interferometer for cosmology
Authors: Karsten Danzmann S. Husa, A. Nairz, B. Pocza, R. Steinbauer
MSC-class: 83C35, 83-05, 83F05
Ref: Proposal to the European Space Agency for a Flexi Mission in Fundamental Physics, (2000).
Download: here

[Mi2] On the geometry of impulsive gravitational waves
Authors: Roland Steinbauer
MSC-class: 46F30, 83C15, 83C35, 46F10
Ref: Prepared for "Proceedings of the 8-th National Romaninan Conference on GRG, Bistritza, June 1998",
which to my best konwledge never appeared
ArXive: gr-qc/9809054

[Mi1] ELFI, A Gravitational Wave Detector for Cosmology
Authors: S. Husa, A. Nairz, B. Pocza, R. Steinbauer
MSC-class: 83C35, 83-05, 83F05
Ref: Fundamental Physics in Space, Proceedings of the Alpbach Summer School 1997, edited by A. Wilson, 45-47 (ESA Publications Division, Noordwijk, 1997).
Download: here

Didactics

[D3] Einführung in das mathematische Arbeiten – der Passage-Point an der Universität Wien
(German; Introduction into mathematical methodology: the passage point at Vienna University)
Authors:Roland Steinbauer, Evelyn Süss-Stepancik, Hermann Schichl
Ref: in Mathematische Vor- und Brückenkurse edited by Bausch, I et al. Springer Spektrum, 2014, 410--424.
Preprint: pdf

[D2] Grenzwert -- quo vadis?
Ein Pilotprojekt zur Analysis-Ausbildung von Lehramtsstudierenden im Unterrichtsfach Mathematik
(German; Limits -- quo vadis? A pilot project in the analysis education in the teacher's curriculum at the University of Vienna)
Authors: Stefan Götz, Roland Steinbauer
Ref: Einreichung zum Lehrpreis Ars docendi 2013 - Staatspreis für exzellente Lehre an den öffentlichen Universitäten Österreichs (Innovative Lehrkonzepte)
Download: pdf

[D1] Einführung in das mathematische Arbeiten: Ein Projekt zur Gestaltung der Studieneingangsphase an der Universität Wien
(German; Introduction into scientific work in mathematics.)
Authors: Hermann Schichl, Roland Steinbauer
Ref: Mitteilungen der DMV (Notices of the German Mathematical Society), 17(4), 244--246, (2009).
Download: pdf

Theses

[H] Nonlinear Distributional Geometry
Authors: Roland Steinbauer
MSC-class: 46F30, 83C35, 83C15, 46F10, 46F05, 83C75
Ref: Habilitationsschrift at the University of Vienna, 2002.
Download: here

[Ph.D.] Distributional Methods in General Relativity
Authors: Roland Steinbauer
MSC-class: 46F30, 83C35, 83C15, 46F10, 46F05, 83C75
Ref: Ph.D. thesis at the University of Vienna, 2000.
Download: here

[M.Sc.] Colombeau Theorie und ultrarelativistischer Limes
Authors: R. Steinbauer
MSC-class: 46F30, 83C35, 83C15, 46F10, 46F05, 83C75
PACS-class: 04.20.Cv, 02.30.Sa, 04.20.Jb, 04.30.-w
Ref: Master's thesis at the University of Vienna, 1995.
Download: here

Editorial Activities

[E1] Special Issue of Integral Transforms and Special Functions
The International Conference on Generalized Functions GF 2009
Editors: Michael Grosser, Michael Kunzinger, Stevan Pilipovic, Roland Steinbauer
Ref: Taylor&Francis, 2011.

Publications listed at arXiv, MathSciNet and ZMAT

You can have a look at my preprints and publications listed at arXiv.org.

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