Date of Graduation
5-2022
Document Type
Dissertation
Degree Name
Doctor of Philosophy in Mathematics (PhD)
Degree Level
Graduate
Department
Mathematical Sciences
Advisor/Mentor
Harrington, Phillip S.
Committee Member
Akeroyd, John R.
Second Committee Member
Raich, Andrew S.
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.
Citation
DeMoulpied, J. (2022). Diederich-Fornæss Index on Boundaries Containing Crescents. Graduate Theses and Dissertations Retrieved from https://scholarworks.uark.edu/etd/4437
Included in
Discrete Mathematics and Combinatorics Commons, Harmonic Analysis and Representation Commons