A note on new weighted geometric inequalities for hypersurfaces in \(\mathbb{R}^n\)

DOI10.1090/PROC/16875MaRDI QIDQ6583774

Jie Wu

Publication date: 6 August 2024

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

zbMATH Keywords

quermassintegralweighted geometric inequalitiesnormalized inverse curvature flow.

Mathematics Subject Classification ID

Higher-dimensional and -codimensional surfaces in Euclidean and related (n)-spaces (53A07) Methods of global Riemannian geometry, including PDE methods; curvature restrictions (53C21)

Cites Work

• An extension of Hsiung-Minkowski formulas and some applications
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• Flow of nonconvex hypersurfaces into spheres
• The quermassintegral inequalities for \(k\)-convex starshaped domains
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• Variational properties of functions of the mean curvatures for hypersurfaces in space forms
• A new monotone quantity along the inverse mean curvature flow in \(\mathbb R^n\)
• Zur Theorie der gemischten Volumina von konvexen Körpern. III: Die Erweiterung zweier Lehrsätze Minkowskis über die konvexen Polyeder auf die beliebigen konvexen Körper.
• Zur Theorie der gemischten Volumina von konvexen Körpern. II: Neue Ungleichungen zwischen den gemischten Volumina und ihre Anwendungen.
• Monotone quantities involving a weighted σ_k integral along inverse curvature flows
• Weighted geometric inequalities for hypersurfaces in sub‐static manifolds
• A Mean Curvature Type Flow in Space Forms
• Geometric inequalities involving three quantities in warped product manifolds
• New weighted geometric inequalities for hypersurfaces in space forms

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