A Steklov eigenvalue estimate for affine connections and its application to substatic triples

2025/04/10 by Fujitani, Yasuaki · 2 citations
#Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2504.07889

Abstract

Choi-Wang obtained a lower bound of the first eigenvalue of the Laplacian on closed minimal hypersurfaces. On minimal hypersurfaces with boundary, Fraser-Li established an inequality giving a lower bound of the first Steklov eigenvalue as a counterpart of the Choi-Wang type inequality. These inequalities were shown under lower bounds of the Ricci curvature. In this paper, under non-negative Ricci curvature associated with an affine connection introduced by Wylie-Yeroshkin, we give a generalization of Fraser-Li type inequality. Our results hold not only for weighted manifolds under non-negative 1-weighted Ricci curvature but also for substatic triples.

Cited by

• Stability of weighted minimal hypersurfaces under a lower 1-weighted Ricci curvature bound
• Choi-Wang inequality for affine connections

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