Harmonic coordinates for the nonlinear Finsler Laplacian and some regularity results for Berwald metrics. (English) Zbl 1432.53024
Summary: We prove existence of harmonic coordinates for the nonlinear Laplacian of a Finsler manifold and apply them in a proof of the Myers-Steenrod theorem for Finsler manifolds. Different from the Riemannian case, these coordinates are not suitable for studying optimal regularity of the fundamental tensor, nevertheless, we obtain some partial results in this direction when the Finsler metric is Berwald.
MSC:
| 53B40 | Local differential geometry of Finsler spaces and generalizations (areal metrics) |
| 58J60 | Relations of PDEs with special manifold structures (Riemannian, Finsler, etc.) |
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