The first Stekloff eigenvalue in weighted Riemannian manifolds

2015/04/10 by Márcio Batista, Batista, M., J. I. Santos +1 · 1 citation
Computer Science · Mathematics · #58C40 #58J50 #Advanced Mathematical Modeling in Engineering #Differential Geometry (math.DG) #FOS: Mathematics #Functional Analysis (math.FA) #Nonlinear Partial Differential Equations #Numerical methods in inverse problems

paper · pdf · doi:10.48550/arxiv.1504.02630

openalex publication_date 2015/04/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In study of eigenvalue problems, a classical problem is the Stekloff eigenvalue problem. There are many estimates of the first non- zero Stekloff eigenvalue, including a sharp estimate on surfaces, obtained by Escobar in "The geometry of the first non-zero Stekloff eigenvalue, J. Funct. Anal. 150 (1997)". In this paper we are interested to study this problem in weighted context. Various estimates are obtained, including a sharp estimate on surfaces, similar to that Escobar obtained.

Citations

• Rigidity of compact manifolds with boundary and nonnegative Ricci curvature

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