A Willmore-type inequality for hypersurfaces with asymptotic or integral Ricci curvature bounds

2025/08/27 by Lee, Jihye
#53A07 #53C21 #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2508.20298

Abstract

We establish Willmore-type inequalities for bounded domains in complete non-compact Riemannian manifolds, under either asymptotic or integral Ricci curvature bounds. Those results recover a recent inequality of Jin-Yin arXiv:2402.02465.

Citations

• Fenchel-Willmore inequality for submanifolds in manifolds with non-negative k-Ricci curvature
• Willmore-type inequalities for closed hypersurfaces in weighted manifolds
• Isoperimetric profile function comparisons with Integral Ricci curvature bounds
• Willmore-type inequality for closed hypersurfaces in complete manifolds with Ricci curvature bounded below
• A sharp geometric inequality for closed hypersurfaces in manifolds with asymptotically nonnegative curvature
• Comparison geometry for substatic manifolds and a weighted Isoperimetric Inequality
• The Log-Sobolev inequality for a submanifold in manifolds with asymptotic non-negative intermediate Ricci curvature
• Sobolev Inequalities In Manifolds With Asymptotically Nonnegative Curvature
• Remark on an inequality for closed hypersurfaces in complete manifolds with nonnegative Ricci curvature
• Sharp geometric inequalities for closed hypersurfaces in manifolds with nonnegative Ricci curvature
• Improved relative volume comparison for integral Ricci curvature and applications to volume entropy
• Boundaries of Zero Scalar Curvature in the AdS/CFT Correspondence
• A Heat Kernel Lower Bound for Integral Ricci Curvature

Related

• Willmore-type inequality for closed hypersurfaces in complete manifolds with Ricci curvature bounded below
• A sharp geometric inequality for closed hypersurfaces in manifolds with asymptotically nonnegative curvature
• Fenchel-Willmore inequality for submanifolds in manifolds with non-negative k-Ricci curvature
• Sharp geometric inequalities for closed hypersurfaces in manifolds with nonnegative Ricci curvature
• Willmore-type inequalities for closed hypersurfaces in weighted manifolds