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arXiv · 2504.07889

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

Yasuaki Fujitani
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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.

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Yasuaki Fujitani. 2025-04-10. A Steklov eigenvalue estimate for affine connections and its application to substatic triples. https://arxiv.org/abs/2504.07889

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