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arXiv · 2507.07655

Fenchel-Willmore inequality for submanifolds in manifolds with non-negative $k$-Ricci curvature

Meng Ji·Kwok-Kun Kwong
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Abstract

We establish a sharp Fenchel-Willmore inequality for closed submanifolds of arbitrary dimension and codimension immersed in a complete Riemannian manifold with non-negative intermediate Ricci curvature and Euclidean volume growth. In the hypersurface case, this reduces to non-negative Ricci curvature. We also characterize the equality case. This generalizes the recent work of Agostiniani, Fogagnolo, and Mazzieri \cite{Agostiniani-Fogagnolo-Mazzieri}, as well as classical results by Chen, Fenchel, Willmore, and others.

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Meng Ji, Kwok-Kun Kwong. 2025-07-10. Fenchel-Willmore inequality for submanifolds in manifolds with non-negative $k$-Ricci curvature. https://arxiv.org/abs/2507.07655

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