Date of Graduation

5-2022

Document Type

Dissertation

Degree Name

Doctor of Philosophy in Mathematics (PhD)

Degree Level

Graduate

Department

Mathematical Sciences

Advisor/Mentor

Phillip Harrington

Committee Member

John Akeroyd

Second Committee Member

Andrew Raich

Keywords

crescent region, automorphisms

Abstract

The worm domain developed by Diederich and Fornæss is a classic example of a boundedpseudoconvex domains that fails to satisfy global regularity of the Bergman Projection, due to the set of weakly pseudoconvex points that form an annulus in its boundary. We instead examine a bounded pseudoconvex domain Ω ⊂ C2 whose set of weakly pseudoconvex points form a crescent in its boundary. In 2019, Harrington had shown that these types of domains satisfy global regularity of the Bergman Projection based on the existence of good vector fields. In this thesis we study the Regularized Diederich-Fornæss index of these domains, another sufficient condition for global regularity of the Bergman Projection.

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