Autor:	René Michel, Marc Arcostanzo
Rok vydání:	1999
Předmět:	Geodesic Mathematical analysis Mathematics::Differential Geometry Geometry and Topology Information geometry Isoperimetric inequality Fundamental theorem of Riemannian geometry Curvature Fisher information metric Convex metric space Mathematics Intrinsic metric
Zdroj:	Geometriae Dedicata. 76:197-209
ISSN:	0046-5755
DOI:	10.1023/a:1005197117909
Popis:	We give a geometrical proof of a Muhometov type inequality, for a single Riemannian metric defined on a closed disc in the plane. We mainly study the case of equality which is achieved if and only if the distance between points on the boundary is invariant under rotation along the boundary. We show that this implies that the metric itself must be invariant under rotation, at least when the metric is analytic or of nonpositive curvature.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::d152acafd1a9aed1798cdcd6ad7103c0 https://doi.org/10.1023/a:1005197117909 Zobrazit plný text záznamu Full text from SpringerLink