Weakly q-Convex Domains and Bounded q-Subharmonic Exhaustion Functions

<p>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. </p>

Name thesis:degree_name

Doctor of Philosophy in Mathematics (PhD)

Level thesis:degree_level

Dissertation

Year dc:date.available

2022

Author dc:creator

• Foss, Emily

Advisor dc:contributor.advisor

• Harrington, Phillip S.

Contributors dc:contributor

• Raich, Andrew S.
• Tjani, Maria

• q-convex
• q-subharmonic
• Mathematics

Repository record dc:identifier

https://scholarworks.uark.edu/etd/4660

OAI identifier oai:identifier

oai:scholarworks.uark.edu:etd-6210