Monotone quantities involving a weighted σk integral along inverse curvature flows

DOI10.1142/S0219199715500145zbMath1325.53086arXiv1402.0843OpenAlexW2963557430MaRDI QIDQ2950145

Kwok-Kun Kwong, Pengzi Miao

Publication date: 8 October 2015

Published in: Communications in Contemporary Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1402.0843

zbMATH Keywords

inverse curvature flow\(\sigma_{k}\) integral

Mathematics Subject Classification ID

Related Items (6)

On an inverse curvature flow in two-dimensional space forms ⋮ Weighted isoperimetric inequalities in warped product manifolds ⋮ Geometric inequalities involving three quantities in warped product manifolds ⋮ Weighted geometric inequalities for hypersurfaces in sub‐static manifolds ⋮ Poincaré type inequality for hypersurfaces and rigidity results ⋮ New weighted geometric inequalities for hypersurfaces in space forms

Cites Work

• On the expansion of starshaped hypersurfaces by symmetric functions of their principal curvatures
• On integral formulas for submanifolds of spaces of constant curvature and some applications
• Some integral formulas for closed hypersurfaces in Riemannian space
• The quermassintegral inequalities for \(k\)-convex starshaped domains
• Compact hypersurfaces with constant higher order mean curvatures
• On the first eigenvalue of the Laplacian for compact submanifolds of Euclidean space
• Stability of hypersurfaces with constant \(r\)-mean curvature
• Integral formulas for the \(r\)-mean curvature linearized operator of a hypersurface
• Convexity estimates for mean curvature flow and singularities of mean convex surfaces
• A new monotone quantity along the inverse mean curvature flow in \(\mathbb R^n\)

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