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

Mo, Xiaohuan; Yang, Yunyan

Sci. China, Ser. A 48, No. 1, 115-130 (2005).

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.

Reviewer: Vladimir Balan (Bucureşti)

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)

Keywords:

harmonic maps; Finsler manifolds; existence; sectional curvature; homotopy class

Citations:

Zbl 0421.31006