Variational Formula for Bergman Kernels

Abstract

For a family of domains $\Omega _t \subset \mathbb{C}^n ,t \in \left[ {0,1} \right]$, a formula for B ₁ (z,s)-B_0(z,s) is established, where B ₀ and B ₁ are the Bergman kernels for $\Omega _0$ and $\Omega _1$. As an application of this formula, we obtain two terms in the asymptotics of B(z,z) as $z \to \partial \Omega$ for a special class of domains. Bibliography: 4 titles.