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.
","abstract_html":"<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>","abstract_has_math":false,"creators":["Foss, Emily"],"institution":null,"degree_name":"Doctor of Philosophy in Mathematics (PhD)","degree_level":"Dissertation","degree_discipline":null,"degree_department":null,"school":null,"contributors":["Raich, Andrew S.","Tjani, Maria"],"advisors":["Harrington, Phillip S."],"committee_chairs":[],"committee_members":[],"year":2022,"date_issued":"2022-08-01T07:00:00Z","date_published":"2022-08-01T07:00:00Z","updated_at":"2026-07-24T01:00:09Z","subjects":["q-convex","q-subharmonic","Mathematics"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://scholarworks.uark.edu/etd/4660","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Raich, Andrew S.","Tjani, Maria"]},{"key":"dc:contributor.advisor","label":"Advisor","values":["Harrington, Phillip S."]},{"key":"dc:creator","label":"Author","values":["Foss, Emily"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2022"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2024-02-06T08:00:00Z"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Dissertation"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Doctor of Philosophy in Mathematics (PhD)"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["q-convex","q-subharmonic","Mathematics"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://scholarworks.uark.edu/etd/4660"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["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.
"]},{"key":"dc:title","label":"Title","values":["Weakly q-Convex Domains and Bounded q-Subharmonic Exhaustion Functions"]}]}],"canonical_facts":{"dc:contributor":["Raich, Andrew S.","Tjani, Maria"],"dc:contributor.advisor":["Harrington, Phillip S."],"dc:creator":["Foss, Emily"],"dc:date":["2022"],"dc:date.available":["2024-02-06T08:00:00Z"],"dc:description.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.
"],"dc:identifier":["https://scholarworks.uark.edu/etd/4660"],"dc:subject":["q-convex","q-subharmonic","Mathematics"],"dc:title":["Weakly q-Convex Domains and Bounded q-Subharmonic Exhaustion Functions"],"thesis:degree_level":["Dissertation"],"thesis:degree_name":["Doctor of Philosophy in Mathematics (PhD)"]},"updated_at":"2026-07-24T01:00:09Z"}