Perturbations of the harmonic map equation

T. Kappeler, S. Kuksin, V. Schroeder

Research output: Contribution to journalArticle

6 Citations (Scopus)

Abstract

We consider perturbations of the harmonic map equation in the case where the target manifold is a closed Riemannian manifold of nonpositive sectional curvature. For any semilinear and, under some extra conditions, quasilinear perturbation, the space of classical solutions within a homotopy class is proved to be compact. An important ingredient for our analysis is a new inequality for maps in a given homotopy class which can be viewed as a version of the Poincaré inequality for such maps.

Original languageEnglish
Pages (from-to)629-669
Number of pages41
JournalCommunications in Contemporary Mathematics
Volume5
Issue number4
DOIs
Publication statusPublished - Aug 2003

Keywords

  • Harmonic maps
  • Nonpositives sectional curvature
  • Short homotopies

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