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.
","abstract_html":"<p>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. </p>","abstract_has_math":false,"creators":["DeMoulpied, Jason"],"institution":null,"degree_name":"Doctor of Philosophy in Mathematics (PhD)","degree_level":"Dissertation","degree_discipline":null,"degree_department":null,"school":null,"contributors":["Akeroyd, John R.","Raich, Andrew S."],"advisors":["Harrington, Phillip S."],"committee_chairs":[],"committee_members":[],"year":2022,"date_issued":"2022-05-01T07:00:00Z","date_published":"2022-05-01T07:00:00Z","updated_at":"2026-07-24T00:59:58Z","subjects":["crescent region","automorphisms","Discrete Mathematics and Combinatorics","Harmonic Analysis and Representation"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://scholarworks.uark.edu/etd/4437","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Akeroyd, John R.","Raich, Andrew S."]},{"key":"dc:contributor.advisor","label":"Advisor","values":["Harrington, Phillip S."]},{"key":"dc:creator","label":"Author","values":["DeMoulpied, Jason"]}]},{"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":["crescent region","automorphisms","Discrete Mathematics and Combinatorics","Harmonic Analysis and Representation"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://scholarworks.uark.edu/etd/4437"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["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.
"]},{"key":"dc:title","label":"Title","values":["Diederich-Fornæss Index on Boundaries Containing Crescents"]}]}],"canonical_facts":{"dc:contributor":["Akeroyd, John R.","Raich, Andrew S."],"dc:contributor.advisor":["Harrington, Phillip S."],"dc:creator":["DeMoulpied, Jason"],"dc:date":["2022"],"dc:date.available":["2024-02-06T08:00:00Z"],"dc:description.abstract":["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.
"],"dc:identifier":["https://scholarworks.uark.edu/etd/4437"],"dc:subject":["crescent region","automorphisms","Discrete Mathematics and Combinatorics","Harmonic Analysis and Representation"],"dc:title":["Diederich-Fornæss Index on Boundaries Containing Crescents"],"thesis:degree_level":["Dissertation"],"thesis:degree_name":["Doctor of Philosophy in Mathematics (PhD)"]},"updated_at":"2026-07-24T00:59:58Z"}