THE UPPER BOUND OF THE HARMONIC MEAN OF THE NEUMANN EIGENVALUES IN CURVED SPACES
Résumé
Considering an n-dimensional Riemannian manifold M whose sectional curvature is bounded above by κ and the Ricci curvature is bounded below by (n − 1)K, we obtain an upper bound for the harmonic mean of the first (n − 1) non-zero Neumann eigenvalues of the Laplace operator for domains contained in M. This can be viewed as certain isoparametric inequality and generalizes the results for domains in the space forms ([Xia-Wang 2022; Benguria-Brandolini-Chiacchio 2020]).
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