Well-posedness of Hersch–Szegő’s center of mass by hyperbolic energy minimization

Autor:	Richard S. Laugesen
Rok vydání:	2021
Předmět:	Unit sphere Geodesic General Mathematics Mathematical analysis Centroid Center of mass Convex function Measure (mathematics) Convexity Energy functional Mathematics
Zdroj:	Annales mathématiques du Québec. 45:363-390
ISSN:	2195-4763 2195-4755
Popis:	The hyperbolic center of mass of a finite measure on the unit ball with respect to a radially increasing weight is shown to exist, be unique, and depend continuously on the measure. Prior results of this type are extended by characterizing the center of mass as the minimum point of an energy functional that is strictly convex along hyperbolic geodesics. A special case is Hersch’s center of mass lemma on the sphere, which follows from convexity of a logarithmic kernel introduced by Douady and Earle.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::b7a0c18f6548f9cd05f43362f7105d2b https://doi.org/10.1007/s40316-020-00151-5 Zobrazit plný text záznamu Full text from SpringerLink