The \(L_p\) John ellipsoids for negative indices

DOI10.1007/s11856-022-2407-2zbMath1523.52003OpenAlexW4310729912MaRDI QIDQ6165164

Xinbao Lu, Ge Xiong

Publication date: 31 July 2023

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

Full work available at URL: https://doi.org/10.1007/s11856-022-2407-2

zbMATH Keywords

convex body\(L_p\) John ellipsoid

Mathematics Subject Classification ID

Convex sets in (n) dimensions (including convex hypersurfaces) (52A20)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Operations between sets in geometry
• Orlicz-John ellipsoids
• The log-Brunn-Minkowski inequality
• \(\mathrm{SL}(n)\) invariant valuations on polytopes
• The Brunn-Minkowski-Firey theory. I: Mixed volumes and the Minkowski problem
• Cone-volume measure of general centered convex bodies
• Orlicz centroid bodies
• General affine surface areas
• The even Orlicz Minkowski problem
• General \(L_{p}\) affine isoperimetric inequalities
• Orlicz projection bodies
• Ellipsoids of maximal volume in convex bodies
• Ellipsoids and matrix-valued valuations
• Extremal problems and isotropic positions of convex bodies
• A new ellipsoid associated with convex bodies
• The \(L^p\)-Busemann-Petty centroid inequality
• \(L_ p\) affine isoperimetric inequalities.
• The logarithmic John ellipsoid
• New affine inequalities and projection mean ellipsoids
• Positions of convex bodies associated to extremal problems and isotropic measures
• Surface bodies and \(p\)-affine surface area
• The Brunn-Minkowski-Firey theory. II: Affine and geominimal surface areas
• Affine isoperimetric inequalities for intersection mean ellipsoids
• Affine images of isotropic measures
• A stability result for mean width of \(L_{p}\)-centroid bodies
• New \(L_p\) affine isoperimetric inequalities
• Cone-volume measures of polytopes
• The \(L_p\)-Minkowski problem and the Minkowski problem in centroaffine geometry
• The Orlicz-Brunn-Minkowski theory: a general framework, additions, and inequalities
• Orlicz-Legendre ellipsoids
• Volume Ratios and a Reverse Isoperimetric Inequality
• Ellipsoids defined by Banach ideal norms
• $L_p$ John Ellipsoids
• On the $L_{p}$-Minkowski problem
• The logarithmic Minkowski problem
• Convex and Discrete Geometry
• Convex Bodies The Brunn-MinkowskiTheory
• Centroid bodies and comparison of volumes