Holder estimates for the $\bar{\partial }$-equation on surfaces with simple singularities

Abstract

Let $\Sigma$ be a 2-dimensional subvariety in $C^3$ with an isolated simple (rational double point) singularity at the origin. The main objective of this paper is to solve the $\dbar$-equation on a neighbourhood of the origin in $\Sigma$, demanding a Holder condition on the solution.

11 pages