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

2025/07/10 by Ji, Meng, Kwong, Kwok-Kun · 2 citations
#53A07 #53C42 #53E10 #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2507.07655

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 \citeAgostiniani-Fogagnolo-Mazzieri, as well as classical results by Chen, Fenchel, Willmore, and others.

Citations

• Proof of the Michael-Simon-Sobolev inequality using optimal transport
• Remark on an inequality for closed hypersurfaces in complete manifolds with nonnegative Ricci curvature
• Sobolev inequalities in manifolds with nonnegative curvature
• Sharp geometric inequalities for closed hypersurfaces in manifolds with nonnegative Ricci curvature
• Volume estimates for tubes around submanifolds using integral curvature\n bounds
• A fully nonlinear flow for two-convex hypersurfaces

Cited by

• Fenchel-Willmore and Sobolev-type inequalities for submanifolds in non-negatively curved manifolds
• A Willmore-type inequality for hypersurfaces with asymptotic or integral Ricci curvature bounds

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• A Willmore-type inequality for hypersurfaces with asymptotic or integral Ricci curvature bounds
• Sharp geometric inequalities for closed hypersurfaces in manifolds with nonnegative Ricci curvature
• A sharp geometric inequality for closed hypersurfaces in manifolds with asymptotically nonnegative curvature