2026-09-19T02:58:00Z https://api.figshare.com/v2/oai

oai:figshare.com:article/30425233 2025-08-01T00:00:00Z portal_693 item_type_8 month_year_08_2025

β-Uniform Convexity and Divisible Domains Amelia Pompilio (22481980) Mathematics 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. 2025-08-01T00:00:00Z Text Thesis 10.25417/uic.30425233.v1 https://figshare.com/articles/thesis/_-Uniform_Convexity_and_Divisible_Domains/30425233 In Copyright