The Hopf-Rinow Theorem in Infinite Dimension.

Abstract

In this paper, the following theorem is proven. Let M be a complete, possibly infinite-dimensional, Riemannian manifold. Take any point q in M. Then the set of points p epsilon M which can be joined to q by a unique minimal geodesic contains a countable intersection of open dense subsets.

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Document Details

Document Type
Technical Report
Publication Date
Oct 01, 1976
Accession Number
ADA034482

Entities

People

  • Ivar Ekeland

Organizations

  • University of Wisconsin–Madison

Tags

DTIC Thesaurus Topics

  • Banach Space
  • Computations
  • Differential Equations
  • Equations
  • Geometry
  • Hilbert Space
  • Identities
  • Inequalities
  • Mathematical Analysis
  • Mathematics
  • Military Research
  • North Carolina
  • Numbers
  • Real Numbers
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  • United States

Fields of Study

  • Mathematics

Readers

  • Graph Algorithms and Convex Optimization.