Work

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

Year: 2025

Type: article

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 inequality. The Fraser-Li type inequality was obtained for manifolds with non-negative Ricci curvature. In this paper, we extend it to the setting of non-negative Ricci curvature with respect to the Wylie-Yeroshkin type affine connection. Our results apply to both weighted Riemannian manifolds with non-negative 1-weighted Ricci curvature and substatic triples.

Source: Analysis and Mathematical Physics

DOI: 10.1007/s13324-025-01135-w

Author: Yasuaki Fujitani

Institution: The University of Osaka

Language: English

Topic: Geometric Analysis and Curvature Flows

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,290

Funders: University of Tokyo, Japan Science and Technology Agency