{"id":{"repo_id":"uic","oai_identifier":"oai:figshare.com:article/30425233"},"canonical_url":"https://search.dev.ndltd.org/etd/uic/oai:figshare.com:article/30425233","repository":{"repo_id":"uic","name":"University of Illinois - Chicago","base_url":"https://api.figshare.com/v2/oai"},"display":{"title":"β-Uniform Convexity and Divisible Domains","abstract":"Divisible convex sets have long been important in the study of Hilbert geometries. When a divisible convex set is an ellipsoid, the Hilbert geometry it induces is the hyperbolic space. In general, strictly convex divisible domains exhibit negative curvature properties, but only the ellipsoid is a CAT(-1) space. The notion of p-uniform convexity from the theory of Banach spaces has been proposed as a generalization of the Alexandrov-Toponogov comparison property to Finsler manifolds. We prove that a natural Finsler metric on a strictly convex divisible domain is β-uniformly convex, where the exact constant β is related to the regularity of the boundary.","abstract_html":"Divisible convex sets have long been important in the study of Hilbert geometries. When a divisible convex set is an ellipsoid, the Hilbert geometry it induces is the hyperbolic space. In general, strictly convex divisible domains exhibit negative curvature properties, but only the ellipsoid is a CAT(-1) space. The notion of p-uniform convexity from the theory of Banach spaces has been proposed as a generalization of the Alexandrov-Toponogov comparison property to Finsler manifolds. We prove that a natural Finsler metric on a strictly convex divisible domain is β-uniformly convex, where the exact constant β is related to the regularity of the boundary.","abstract_has_math":false,"creators":["Amelia Pompilio (22481980)"],"institution":null,"degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2025,"date_issued":"2025-08-01T00:00:00Z","date_published":"2025-08-01T00:00:00Z","updated_at":"2026-07-27T21:34:50Z","subjects":["Mathematics"],"languages":[],"rights":["In Copyright"],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://doi.org/10.25417/uic.30425233.v1","outbound_label":"DOI","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:creator","label":"Author","values":["Amelia Pompilio (22481980)"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2025-08-01T00:00:00Z"]},{"key":"dc:relation","label":"Dc Relation","values":["https://figshare.com/articles/thesis/_-Uniform_Convexity_and_Divisible_Domains/30425233"]},{"key":"dc:type","label":"Dc Type","values":["Text","Thesis"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Mathematics"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:rights","label":"Dc Rights","values":["In Copyright"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["10.25417/uic.30425233.v1"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["Divisible convex sets have long been important in the study of Hilbert geometries. When a divisible convex set is an ellipsoid, the Hilbert geometry it induces is the hyperbolic space. In general, strictly convex divisible domains exhibit negative curvature properties, but only the ellipsoid is a CAT(-1) space. The notion of p-uniform convexity from the theory of Banach spaces has been proposed as a generalization of the Alexandrov-Toponogov comparison property to Finsler manifolds. We prove that a natural Finsler metric on a strictly convex divisible domain is β-uniformly convex, where the exact constant β is related to the regularity of the boundary."]},{"key":"dc:title","label":"Title","values":["β-Uniform Convexity and Divisible Domains"]}]}],"canonical_facts":{"dc:creator":["Amelia Pompilio (22481980)"],"dc:date":["2025-08-01T00:00:00Z"],"dc:description":["Divisible convex sets have long been important in the study of Hilbert geometries. When a divisible convex set is an ellipsoid, the Hilbert geometry it induces is the hyperbolic space. In general, strictly convex divisible domains exhibit negative curvature properties, but only the ellipsoid is a CAT(-1) space. The notion of p-uniform convexity from the theory of Banach spaces has been proposed as a generalization of the Alexandrov-Toponogov comparison property to Finsler manifolds. We prove that a natural Finsler metric on a strictly convex divisible domain is β-uniformly convex, where the exact constant β is related to the regularity of the boundary."],"dc:identifier":["10.25417/uic.30425233.v1"],"dc:relation":["https://figshare.com/articles/thesis/_-Uniform_Convexity_and_Divisible_Domains/30425233"],"dc:rights":["In Copyright"],"dc:subject":["Mathematics"],"dc:title":["β-Uniform Convexity and Divisible Domains"],"dc:type":["Text","Thesis"]},"updated_at":"2026-07-27T21:34:50Z"}