p-Laplacian first eigenvalues controls on Finsler manifolds

2017/03/21 by Cyrille Combete, Combete, Cyrille, Serge Degla +3 · 1 citation
Mathematics · Physics and Astronomy · #35P15 #58B20 #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows

paper · pdf · doi:10.48550/arxiv.1704.01402

openalex publication_date 2017/03/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Given a Finsler manifold (M,F), it is proved that the first eigenvalue of the Finslerian p-Laplacian is bounded above by a constant depending on p, the dimension of M, the Busemann-Hausdorff volume and the reversibility constant of (M,F). For a Randers manifold (M,F:=√(g)+β), where g is a Riemannian metric on M and β an appropriate 1-form on M, it is shown that the first eigenvalue λ_1,p(M,F) of the Finslerian p-Laplacian defined by the Finsler metric F is controled by the first eigenvalue λ_1,p(M,g) of the Riemannian p-Laplacian defined on (M,g). Finally, the Cheeger's inequality for Finsler Laplacian is extended for p-Laplacian, with p > 1.

Citations

• Cheeger's constant and the first eigenvalue of a closed Finsler manifold

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• Optimal Hardy-weights for the Finsler p-Dirichlet integral with a potential

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