A SHARP LOWER BOUND OF THE FIRST NEUMANN EIGENVALUE OF A COMPACT HYPERSURFACE INSIDE A CONVEX SET

Abstract

In this paper we provide a sharp lower bound of the first Neumann eigenvalue of a compact hypersurface Σ inside a convex set C in a Riemannian manifold under the assumption that ∂Σ meets ∂C orthogonally.

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