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Harmonic Coordinates for the Nonlinear Finsler Laplacian and Some Regularity Results for Berwald Metrics

Department of Mechanics, Mathematics and Management, Politecnico di Bari, Via Orabona 4, 70125 Bari, Italy
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Axioms 2019, 8(3), 83; https://doi.org/10.3390/axioms8030083
Received: 22 June 2019 / Revised: 16 July 2019 / Accepted: 17 July 2019 / Published: 23 July 2019
(This article belongs to the Special Issue Geometric Analysis and Mathematical Physics)
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. View Full-Text
Keywords: Finsler Laplacian; harmonic coordinates; regularity; Berwald Finsler Laplacian; harmonic coordinates; regularity; Berwald
MDPI and ACS Style

Caponio, E.; Masiello, A. Harmonic Coordinates for the Nonlinear Finsler Laplacian and Some Regularity Results for Berwald Metrics. Axioms 2019, 8, 83.

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