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The existence of harmonic maps from Finsler manifolds to Riemannian manifolds. (English) Zbl 1127.58011

The paper investigates the existence of harmonic maps from Finsler manifolds to Riemannian manifolds, and their characterization in the spirit of [T. Ishihara, J. Math. Kyoto Univ., No. 19, 215–229 (1979; Zbl 0421.31006)]. Using the heat equation method, it is shown that any smooth map from a compact Finsler manifold to a compact Riemannian manifold with non-positive sectional curvature is homotopic to a harmonic map which has the minimal energy in its homotopy class.

MSC:

58E20 Harmonic maps, etc.
53C43 Differential geometric aspects of harmonic maps
53C44 Geometric evolution equations (mean curvature flow, Ricci flow, etc.) (MSC2010)
53C60 Global differential geometry of Finsler spaces and generalizations (areal metrics)

Citations:

Zbl 0421.31006
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