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The existence of harmonic maps from Finsler manifolds to Riemannian manifolds

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Abstract

In this paper, we consider the existence of harmonic maps from a Finsler manifold and study the characterisation of harmonic maps, in the spirit of Ishihara. Using heat equation method we show that any map from a compact Finsler manifold M to a compact Riemannian manifold with non-positive sectional curvature can be deformed into a harmonic map which has minimum energy in its homotopy class.

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Authors and Affiliations

  1. LMAM, School of Mathematical Sciences, Peking University, 100871, Beijing, China

    Xiaohuan Mo

  2. Department of Mathematics, Renmin University of China, 100872, Beijing, China

    Yunyan Yang

Authors
  1. Xiaohuan Mo
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  2. Yunyan Yang
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Correspondence to Xiaohuan Mo.

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Mo, X., Yang, Y. The existence of harmonic maps from Finsler manifolds to Riemannian manifolds. Sci. China Ser. A-Math. 48, 115–130 (2005). https://doi.org/10.1360/03ys0338

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  • DOI: https://doi.org/10.1360/03ys0338

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