Compact manifolds with fixed boundary and large Steklov eigenvalues

2017/01/15 by Bruno Colbois, Colbois, Bruno, Ahmad El Soufi +3 · 1 citation
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Spectral Theory (math.SP) #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.1701.04125

openalex publication_date 2017/01/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let M be a compact Riemannian manifold with boundary. Let b&gt;0 be the number of connected components of its boundary. For manifolds of dimension at least 3, we prove that it is possible to obtain an arbitrarily large (b+1)-th Steklov eigenvalue using a smooth conformal perturbation which is supported in a thin neighbourhood of the boundary, identically equal to 1 on the boundary. For j<b></b>

Citations

• Comparison of Steklov eigenvalues on a domain and Laplacian eigenvalues on its boundary in Riemannian manifolds

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