Variational Formula for Bergman Kernels

For a family of domains W_t ì mathbbCⁿ ,t ? [ 0,1 ]Omega _t subset mathbb{C}^n ,t in left[ {0,1} right], a formula for B₁(z,s)-B_0(z,s) is established, where B₀ and B₁ are the Bergman kernels for W₀Omega _0 and W₁Omega _1. As an application of this formula, we obtain two terms in the asymptotics of B(z,z) as z ? ?Wz to partial Omega for a special class of domains. Bibliography: 4 titles.