Date of Graduation
Doctor of Philosophy in Mathematics (PhD)
Second Committee Member
crescent region, automorphisms
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.
DeMoulpied, J. (2022). Diederich-Fornæss Index on Boundaries Containing Crescents. Graduate Theses and Dissertations Retrieved from https://scholarworks.uark.edu/etd/4437