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Willmore-type inequality for closed hypersurfaces in complete manifolds with Ricci curvature bounded below
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abstract
In this paper, we establish a Willmore-type inequality for closed hypersurfaces in a complete Riemannian manifold of dimension $n+1$ with ${\rm Ric}\geq-ng$. It extends the classic result of Argostianiani, Fogagnolo, and Mazzieri in [1] to the Riemannian manifold of negative curvature. As an application, we construct a Willmore-type inequality for closed hypersurfaces in hyperbolic space and obtain the characterization of geodesic sphere.
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Estimates of $p$-capacity for manifolds with Ricci curvature bounded from below
Sharp p-capacity comparison inequalities in terms of boundary mean curvature on manifolds with Ric ≥ -ng and Ric ≥ 0, with equality forcing warped-product rigidity, plus optimal normalization thresholds for scale-inva...
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