What Do ‘Convexities’ Imply on Hadamard Manifolds?

A. Kristály, Chong Li, Genaro López-Acedo, Adriana Nicolae

Research output: Contribution to journalArticle

7 Citations (Scopus)

Abstract

Various results based on some convexity assumptions (involving the exponential map along with affine maps, geodesics and convex hulls) have been recently established on Hadamard manifolds. In this paper, we prove that these conditions are mutually equivalent and they hold, if and only if the Hadamard manifold is isometric to the Euclidean space. In this way, we show that some results in the literature obtained on Hadamard manifolds are actually nothing but their well-known Euclidean counterparts.

Original languageEnglish
Pages (from-to)1-7
Number of pages7
JournalJournal of Optimization Theory and Applications
DOIs
Publication statusAccepted/In press - May 25 2016

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Keywords

  • Affin function
  • Convex hull
  • Convexity
  • Hadamard manifold

ASJC Scopus subject areas

  • Applied Mathematics
  • Control and Optimization
  • Management Science and Operations Research

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