Date of Graduation
8-2022
Document Type
Dissertation
Degree Name
Doctor of Philosophy in Mathematics (PhD)
Degree Level
Graduate
Department
Mathematical Sciences
Advisor/Mentor
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