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Annals of Global Analysis and Geometry

, Volume 33, Issue 2, pp 101–113 | Cite as

A note on Morse inequalities for harmonic maps with potential and their applications

  • Gerasim KokarevEmail author
Original Paper
  • 83 Downloads

Abstract

We discuss Morse inequalities for homotopic critical maps of the energy functional with a potential term. For a generic potential this gives a lower bound on the number of homotopic critical maps in terms of the Betti numbers of the moduli space of harmonic maps. Other applications include sharp existence results for maps with prescribed tension field and pseudo-harmonic maps. Our hypotheses are that the domain and target manifolds are closed and the latter has non-positive sectional curvature.

Keywords

Morse inequalities Harmonic maps with potential Moduli space of harmonic maps 

Mathematics Subject Classifications (2000)

58E20 58E05 58E50 

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Copyright information

© Springer Science + Business Media B.V. 2007

Authors and Affiliations

  1. 1.School of MathematicsThe University of EdinburghEdinburghUK

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