A natural Finsler-Laplace operator

DOI10.1007/S11856-012-0168-ZzbMath1329.53106arXiv1104.4326OpenAlexW2145449329MaRDI QIDQ375893

Thomas Barthelmé

Publication date: 1 November 2013

Published in: Israel Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1104.4326

zbMATH Keywords

spectrumLaplace operatorFinsler metricsKatok-Ziller metrics

Mathematics Subject Classification ID

Relations of PDEs with special manifold structures (Riemannian, Finsler, etc.) (58J60) Global differential geometry of Finsler spaces and generalizations (areal metrics) (53C60)

Related Items (9)

Eigenvalue control for a Finsler-Laplace operator ⋮ The maximum diam theorem on Finsler manifolds ⋮ Geodesic random walks, diffusion processes and Brownian motion on Finsler manifolds ⋮ Laplacian and spectral gap in regular Hilbert geometries ⋮ Some Liouville-type theorems for harmonic functions on Finsler manifolds ⋮ On deformations of the spectrum of a Finsler-Laplacian that preserve the length spectrum ⋮ Comparison theorems and their applications on Kähler Finsler manifolds ⋮ Laplace Beltrami operator in the Baran metric and pluripotential equilibrium measure: the ball, the simplex, and the sphere ⋮ Semicontinuity of eigenvalues under intrinsic flat convergence

Cites Work

• The Dirichlet problem at infinity for a negatively curved manifold
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• Heat kernel bounds, conservation of probability and the Feller property
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• Projectively flat Finsler 2-spheres of constant curvature
• A sphere theorem for non-reversible Finsler metrics
• Zermelo navigation on Riemannian manifolds
• Perturbation theory for linear operators.
• Le spectre d'une variété riemannienne. (The spectrum of a Riemannian manifold)
• The existence of two closed geodesics on every Finsler 2-sphere
• FINSLER LAPLACIANS AND MINIMAL-ENERGY MAPS
• Locally symmetric Finsler spaces in negative curvature
• Ergodic properties of Brownian motion on covers of compact negatively-curve manifolds
• Geometry of the Katok examples
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