Harmonic maps on complete manifolds

Abstract

In this article, we study harmonic maps between two complete non-compact manifolds M and N by a heat flow method. We find some new sufficient conditions to ensure the uniform convergence of the heat flow, and hence the existence of harmonic maps. Our conditions are: The Ricci curvature of M is bounded from below by a negative constant, M admits a positive Green's function, and ∫M G(x,y)|τ(h(y))|dVy is bounded on each compact subset. where τ(h(x)) is the tension field of the initial data h(x). Conditions (1) are somewhat sharp as is shown by examples in the paper.

Department(s)

Mathematics

Document Type

Article

DOI

https://doi.org/10.3934/dcds.1999.5.799

Keywords

Harmonic maps between complete, Heat flow method, Noncompact manifolds, Uniform convergence of heat flows

Publication Date

1-1-1999

Journal Title

Discrete and Continuous Dynamical Systems

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