OnLp-Affine Surface Area and Curvature Measures

DOI10.1093/imrn/rnv178zbMath1343.52006arXiv1509.05485OpenAlexW3098371466MaRDI QIDQ2800173

Yiming Zhao

Publication date: 15 April 2016

Published in: International Mathematics Research Notices (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1509.05485

zbMATH Keywords

curvature measuresupper semi-continuityaffine surface areaaffine isoperimetric inequality

Mathematics Subject Classification ID

Classes of sets (Borel fields, (sigma)-rings, etc.), measurable sets, Suslin sets, analytic sets (28A05) Length, area, volume, other geometric measure theory (28A75) Length, area, volume and convex sets (aspects of convex geometry) (52A38) Convex sets in (n) dimensions (including convex hypersurfaces) (52A20) Affine differential geometry (53A15) Inequalities and extremum problems in real or complex geometry (51M16)

Related Items (12)

\(L_p\)-curvature measures and \(L_{p, q}\)-mixed volumes ⋮ Constrained convex bodies with extremal affine surface areas ⋮ The Orlicz Minkowski Problem for general measures ⋮ The Orlicz Minkowski problem for cone-volume measure ⋮ The \(L_p\) chord Minkowski problem ⋮ The dual Orlicz-Minkowski problem ⋮ \(L_{p}\) dual curvature measures ⋮ Flag numbers and floating bodies ⋮ Some \(\log\)-Minkowski inequalities for \(L_p\)-mixed affine surface area ⋮ New sine ellipsoids and related volume inequalities ⋮ Some inequalities for the (p, q)-mixed affine surface areas ⋮ The dual Minkowski problem for symmetric convex bodies

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