Klas Diederich, John Erik Fornęss, Sophia Vassiliadou
Local L$^2$ Results for $\overline{\partial}$ on a Singular Surface
Preprint series: ESI preprints

MSC:

32B10 Germs of analytic sets

Abstract: The Cauchy-Riemann equations are fundamental in complex analysis.
This paper contributes to the understanding of these equations on
singular spaces.
Various methods have been used to overcome the problem of defining
forms near singularities. One can blow up the singularity, restrict
forms from smooth ambient spaces or work on the regular points. In this
article we use the latter approach to obtain square integrable solutions
on singular surfaces. This can be briefly called the Kohn solution
up to the singularity to contrast with results in terms of curvature,
weights or different function spaces.
Keywords: Singularity, Cauchy-Riemann equation, Cohomology Groups