The upper bound of the harmonic mean of the Steklov eigenvalues in curved spaces

Abstract

AbstractConsidering an ‐dimensional Riemannian manifold whose sectional curvature is bounded above by and Ricci curvature is bounded below by , we obtain an upper bound of the harmonic mean of the first nonzero Steklov eigenvalues for domains contained in . This can be viewed as certain isoperimetric inequality and generalizes the result on comparing the first nonzero Steklov eigenvalues for such domains (Li–Wang–Wu, 2020, arXiv:2003.03093).