The Bergman kernel on Reinhardt domains

Chieh-Hsien Tiao, Purdue University

Abstract

In the first chapter, we calculate the Bergman Kernel of monomial polyhedron P by splitting the index space ${\cal N}\sp{n}$ into finite disjoint convex cones which correspond to faces ${\cal F}(w)$ of $\partial {\rm log}(P).$ This enables us to sum up the index within the cones individually, and yields an estimate for the Bergman kernel of monomial polyhedron P on diagonal. In the second chapter, in order to calculate the Bergman kernel for a smooth pseudoconvex Reinhardt domain $\Omega$ of finite type, we first show that any pseudoconvex polynomial is roughly equivalent to a polynomial with all coefficients positive. This enables us to approximate $\Omega$ by certain type of monomial polyhedron, and leads to a conjecture for the Bergman kernel on smooth pseudoconvex Reinhardt domains.

Degree

Ph.D.

Advisors

Catlin, Purdue University.

Subject Area

Mathematics

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