Local properties of geodesics on \(p\)-convex sets
type: Item
instance of: scholarly article
title: Local properties of geodesics on \(p\)-convex sets
zbMATH Open document ID: 0767.53033
DOI: 10.1007/BF01766291
author: Annamaria Canino
published in: Annali di Matematica Pura ed Applicata. Serie Quarta
publication date: 1992-09-27T00:00:00Z
review text: Let \(M\) be a set of points of a Hilbert space \(H\) and \(p: M\to\mathbb{R}^ +\) be continuous. \(M\) is said to be a \(p\)-convex set iff \((a,v-u)\leq p(u)| a| | v-u|^ 2\) whenever \(u,v\in M\) and \(a\in \partial^ - I_ M(u)\), where \(\partial^ - I_ M(u)\) denotes a closed convex cone to \(M\) at \(u\) in \(H\). After proving some local properties of geodesics on \(p\)-convex sets the author gives an intrinsic characterization of geodesics in terms of local minimality for the energy functional, proves local uniqueness and continuous dependence on extrema for geodesics with assigned endpoints, and shows some consequences of these results.
Mathematics Subject Classification ID: 53C22
Mathematics Subject Classification ID: 52A05
zbMATH DE Number: 59763
zbMATH Keywords: Hilbert space
zbMATH Keywords: energy functional
reviewed by: Włodzimierz Waliszewski
MaRDI profile type: Publication
cites work: The Riemannian obstacle problem
cites work: Q3782303
cites work: On p-convex sets and geodesics
cites work: Existence of a closed geodesic on p-convex sets
cites work: Q3353469
cites work: Q3730508
cites work: Q3917070
cites work: Q3670036
cites work: General properties of \((p,q)\)-convex functions and \((p,q)\)-monotone operators
cites work: Evolution equations with lack of convexity
cites work: Nonconvex minimization problems
cites work: Q3676777
cites work: Strong Rigidity of Locally Symmetric Spaces. (AM-78)
cites work: Existence and multiplicity of geodesics with constraints and varying end points
cites work: Q3736502
full work available at URL: https://doi.org/10.1007/bf01766291
OpenAlex ID: W2079042675
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description: scientific article; zbMATH DE number 59763