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

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.