On Aleksandrov-Fenchel inequalities for \(k\)-convex domains

DOI10.1007/s00032-011-0159-2zbMath1229.52002OpenAlexW1983995727MaRDI QIDQ640703

Yi Wang, Sun Yung Alice Chang

Publication date: 19 October 2011

Published in: Milan Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00032-011-0159-2

zbMATH Keywords

mixed volumeAleksandrov-Fenchel inequalityquermassintegraloptimal transport mapMichael-Simon inequality

Mathematics Subject Classification ID

Higher-dimensional and -codimensional surfaces in Euclidean and related (n)-spaces (53A07) Mixed volumes and related topics in convex geometry (52A39) Convex sets in (n) dimensions (including convex hypersurfaces) (52A20)

Related Items (19)

Minkowski inequalities via nonlinear potential theory ⋮ Gauss-Bonnet-Chern mass and Alexandrov-Fenchel inequality ⋮ The dual difference Aleksandrov-Fenchel inequality ⋮ Michael-Simon inequalities for \(k\)-th mean curvatures ⋮ Geometric aspects of \(p\)-capacitary potentials ⋮ Mass, center of mass and isoperimetry in asymptotically flat 3-manifolds ⋮ Stability of quermassintegral inequalities along inverse curvature flows ⋮ A fractional Michael-Simon Sobolev inequality on convex hypersurfaces ⋮ Willmore inequality on hypersurfaces in hyperbolic space ⋮ Inequalities for quermassintegrals on \(k\)-convex domains ⋮ A new mass for asymptotically flat manifolds ⋮ The GBC mass for asymptotically hyperbolic manifolds ⋮ Isoperimetric type problems and Alexandrov-Fenchel type inequalities in the hyperbolic space ⋮ The Gauss-Bonnet-Chern mass for graphic manifolds ⋮ A volume-preserving anisotropic mean curvature type flow ⋮ Monotonicity formulas in potential theory ⋮ Aleksandrov-Fenchel inequalities for unitary valuations of degree 2 and 3 ⋮ A family of higher-order isoperimetric inequalities ⋮ Universal Hardy–Sobolev inequalities on hypersurfaces of Euclidean space

Cites Work

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• Geometric inequalities on locally conformally flat manifolds
• Isoperimetric inequalities for quermassintegrals
• Existence and uniqueness of monotone measure-preserving maps
• Regularity of potential functions of the optimal transportation problem
• On the Hessian of a function and the curvature of its graph
• Polar factorization and monotone rearrangement of vector‐valued functions
• The Regularity of Mappings with a Convex Potential
• Boundary regularity of maps with convex potentials
• Sobolev and mean‐value inequalities on generalized submanifolds of Rⁿ
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