Boundary behavior of the Bergman curvature in strictly pseudoconvex polyhedral domains

Abstract

In this article, we present an explicit description of the boundary behavior of the holomorphic curvature of the Bergman metric of bounded strictly pseudoconvex polyhedral domains with piecewise C2 smooth boundaries. Such domains arise as an intersection of domains with strongly pseudoconvex domains with C2 smooth boundaries, creating normal singularities in the boundary. Our results in particular yield an optimal generalization of the well-known theorem of Klembeck, in terms of the boundary regularity. As an application, we demonstrate generalization of several theorems which were previously known only for the cases of eveywhere C°° (essentially) smooth boundaries.