Date of Graduation
8-2022
Document Type
Dissertation
Degree Name
Doctor of Philosophy in Mathematics (PhD)
Degree Level
Graduate
Department
Mathematical Sciences
Advisor
Phillip S. Harrington
Committee Member
Andrew S. Raich
Second Committee Member
Maria Tjani
Keywords
q-convex, q-subharmonic
Abstract
We generalize the Diederich-Fornaess index to bounded weakly q-convex domains with bounded q-subharmonic exhaustion functions. Sufficient conditions for this generalized Diederich-Fornæss index to have a given lower bound are proved. We show this generalized index is positive on bounded weakly q-convex domains with C^3 boundaries. Additionally, we prove sufficient conditions for this generalized index to equal one. For example, we show that if the domain has Property ( ̃(Pq ) ) then the domain has high hyperconvexity.
Citation
Foss, E. (2022). Weakly q-Convex Domains and Bounded q-Subharmonic Exhaustion Functions. Graduate Theses and Dissertations Retrieved from https://scholarworks.uark.edu/etd/4660