The logarithmic Minkowski problem for non-symmetric measures

DOI10.1090/tran/7499zbMath1406.52018OpenAlexW2781803535MaRDI QIDQ4645095

Shibing Chen, Guangxian Zhu, Qi-Rui Li

Publication date: 10 January 2019

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

Full work available at URL: https://doi.org/10.1090/tran/7499

zbMATH Keywords

cone-volume measurelogarithmic Minkowski problemsubspace concentration condition

Mathematics Subject Classification ID

Inequalities and extremum problems involving convexity in convex geometry (52A40) Singular elliptic equations (35J75) Monge-Ampère equations (35J96)

Related Items (46)

Existence of solution for Lp-Minkowski problem of 0 < p < 1 with measures in ℝn ⋮ The logarithmic John ellipsoid ⋮ Multiple solutions of the planar \(L_p\) dual Minkowski problem ⋮ A flow approach to the Musielak-Orlicz-Gauss image problem ⋮ The discrete Orlicz-Minkowski problem for \(p\)-capacity ⋮ Smooth solutions to the Gauss image problem ⋮ The \(L_p\) Gauss image problem ⋮ On the \(L^p\) Aleksandrov problem for negative \(p\) ⋮ Equivalence of the local and global versions of the \(L^p\)-Brunn-Minkowski inequality ⋮ The discrete logarithmic Minkowski problem for \(q\)-capacity ⋮ The \(L_p\)-Brunn-Minkowski inequality for \(p<1\) ⋮ Necessary subspace concentration conditions for the even dual Minkowski problem ⋮ Log-Brunn-Minkowski inequality under symmetry ⋮ The log-Minkowski inequality of curvature entropy ⋮ On the \(L_p\) Gaussian Minkowski problem ⋮ Notes on the log-Brunn-Minkowski inequality ⋮ Affine subspace concentration conditions for centered polytopes ⋮ Flow by 𝜎_{𝑘} curvature to the Orlicz Christoffel-Minkowski problem ⋮ A flow approach to the planar Lp$L_p$ Minkowski problem ⋮ On subspace concentration for dual curvature measures ⋮ Variational analysis of the planar \(L_p\) dual Minkowski problem ⋮ Convex hypersurfaces with prescribed Musielak-Orlicz-Gauss image measure ⋮ Flow by Gauss curvature to the \(L_p\) dual Minkowski problem ⋮ Subspace concentration of mixed volume measures ⋮ A \(L_p\) Brunn-Minkowski theory for logarithmic capacity ⋮ The \(L_{p}\) dual Minkowski problem for \(p\) 1 and \(q\) 0 ⋮ A flow method for the dual Orlicz–Minkowski problem ⋮ General volumes in the Orlicz-Brunn-Minkowski theory and a related Minkowski problem. II ⋮ The Minkowski problem in Gaussian probability space ⋮ \(C^{1,1}\) regularity for solutions to the degenerate \(L_p\) dual Minkowski problem ⋮ Variations of a class of Monge-Ampère-type functionals and their applications ⋮ The \(L_p\) dual Minkowski problem and related parabolic flows ⋮ Stable solution of the Logarithmic Minkowski problem in the case of hyperplane symmetries ⋮ Sharp affine isoperimetric inequalities for the volume decomposition functionals of polytopes ⋮ Smoothness in the \(L_p\) Minkowski problem for \(p<1\) ⋮ The \(L_p\) Minkowski problem for torsion ⋮ The 𝐿_{𝑝} Aleksandrov problem for origin-symmetric polytopes ⋮ Existence of smooth even solutions to the dual Orlicz-Minkowski problem ⋮ The \(L _p\) capacitary Minkowski problem for polytopes ⋮ A class of Gauss curvature flows and its applications to an even dual Orlicz-Minkowski type problem ⋮ The dual Minkowski problem for symmetric convex bodies ⋮ The L_p Minkowski problem for q-capacity ⋮ The Orlicz version of the \(L_p\) Minkowski problem for \(- n < p < 0\) ⋮ Uniqueness of solutions to the logarithmic Minkowski problem in \(\mathbb{R}^3\) ⋮ The logarithmic capacitary Minkowski problem for polytopes ⋮ The planar \(L_{p}\)-Minkowski problem for \(0<p<1\)

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