Diederich-Fornæss Index on Boundaries Containing Crescents

<p>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. </p>

Name thesis:degree_name

Doctor of Philosophy in Mathematics (PhD)

Level thesis:degree_level

Dissertation

Year dc:date.available

2022

Author dc:creator

• DeMoulpied, Jason

Advisor dc:contributor.advisor

• Harrington, Phillip S.

Contributors dc:contributor

• Akeroyd, John R.
• Raich, Andrew S.

• crescent region
• automorphisms
• Discrete Mathematics and Combinatorics
• Harmonic Analysis and Representation

Repository record dc:identifier

https://scholarworks.uark.edu/etd/4437

OAI identifier oai:identifier

oai:scholarworks.uark.edu:etd-5987