Convergence to a geodesic
type: Item
instance of: scholarly article
title: Convergence to a geodesic
zbMATH Open document ID: 0813.53028
author: Norihito Koiso
published in: Osaka Journal of Mathematics
publication date: 1994-07-07T00:00:00Z
review text: The equation \((d/dt) (c_ t)= D_{\dot c_ t}\dot c_ t\) (ES), a semi-linear heat equation, was studied by Eels and Sampson [\textit{J. Eels jun.} and \textit{J. H. Sampson}, Am. J. Math. 86, 109-160 (1964; Zbl 0122.401)]. They proved that for a compact Riemannian manifold \((M,g)\), with nonpositive sectional curvature, a solution \(c_ t\) exists for all time and a subsequence \(c_{t_ i}\) converges to a geodesic. The author shows that under a natural condition (\(C^ \infty\) initial data) the above curvature restriction is not necessary and the equation (ES) has a unique solution \(c_ t\); moreover, if \((M,g)\) is real analytic then the solution converges to a geodesic.
reviewed by: Valentin Boju
Mathematics Subject Classification ID: 53C22
Mathematics Subject Classification ID: 37C10
zbMATH DE Number: 579213
zbMATH Keywords: Cauchy problem
zbMATH Keywords: semi-linear heat equation
zbMATH Keywords: geodesic
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 579213