A note on Morse inequalities for harmonic maps with potential and their applications
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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.
KeywordsMorse inequalities Harmonic maps with potential Moduli space of harmonic maps
Mathematics Subject Classifications (2000)58E20 58E05 58E50
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