Geometry of log-concave functions: the \(L_p\) Asplund sum and the \(L_p\) Minkowski problem

DOI10.1007/s00526-021-02155-7zbMath1494.26018arXiv2006.16959OpenAlexW4226300783WikidataQ114018024 ScholiaQ114018024MaRDI QIDQ2113294

Deping Ye, Niufa Fang, Sudan Xing

Publication date: 14 March 2022

Published in: Calculus of Variations and Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2006.16959

Mathematics Subject Classification ID

Inequalities and extremum problems involving convexity in convex geometry (52A40) Convexity of real functions of several variables, generalizations (26B25) Inequalities involving derivatives and differential and integral operators (26D10)

Related Items

On the framework of \(L_p\) summations for functions ⋮ \textit{A priori} bounds, existence, and uniqueness of smooth solutions to an anisotropic \(L_p\) Minkowski problem for log-concave measure ⋮ Continuity of the solution to the \(L_p\) Minkowski problem in Gaussian probability space

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Mirror symmetric solutions to the centro-affine Minkowski problem
• Dealing with moment measures via entropy and optimal transport
• Rogers-Shephard inequality for log-concave functions
• Support functions and mean width for \(\alpha\)-concave functions
• Real Monge-Ampère equations and Kähler-Ricci solitons on toric log Fano varieties
• Functional affine-isoperimetry and an inverse logarithmic Sobolev inequality
• The Brunn-Minkowski-Firey theory. I: Mixed volumes and the Minkowski problem
• Affine isoperimetric inequalities in the functional Orlicz-Brunn-Minkowski theory
• Some functional inverse Santaló inequalities
• Critères de convexité et inégalités intégrales
• On extensions of the Brunn-Minkowski and Prekopa-Leindler theorems, including inequalities for log concave functions, and with an application to the diffusion equation
• On solvability of two-dimensional \(L_{p}\)-Minkowski problem.
• Isoperimetric and analytic inequalities for log-concave probability measures
• LYZ ellipsoid and Petty projection body for log-concave functions
• General volumes in the Orlicz-Brunn-Minkowski theory and a related Minkowski problem. I
• John's ellipsoid and the integral ratio of a log-concave function
• The dual Orlicz-Minkowski problem
• A reverse Rogers-Shephard inequality for log-concave functions
• On the regularity of solutions to a generalization of the Minkowski problem
• Mixed integrals and related inequalities
• Rotationally symmetric solutions to the \(L_p\)-Minkowski problem
• A Riesz representation theorem for functionals on log-concave functions
• Functional Brunn-Minkowski inequalities induced by polarity
• An extension of Berwald's inequality and its relation to Zhang's inequality
• Rogers-Shephard and local Loomis-Whitney type inequalities
• Moment measures
• The \(L_p\) Minkowski problem for polytopes for \(0 < p < 1\)
• Nonuniqueness of solutions to the \(L_p\)-Minkowski problem
• On the uniqueness of \(L_p\)-Minkowski problems: the constant \(p\)-curvature case in \(\mathbb{R}^3\)
• \(L_p\) Minkowski problem with not necessarily positive data
• Some functional forms of Blaschke-Santaló inequality
• The concept of duality in convex analysis, and the characterization of the Legendre transform
• Affine Orlicz Pólya-Szegő principle for log-concave functions
• Log-concave functions
• Differential analysis of polarity: polar Hamilton-Jacobi, conservation laws, and Monge Ampère equations
• Floating functions
• Stability of the functional forms of the Blaschke-Santaló inequality
• The first variation of the total mass of log-concave functions and related inequalities
• Divergence for \(s\)-concave and log concave functions
• On the \(L_{p}\) Minkowski problem for polytopes
• The \(L_p\)-Minkowski problem and the Minkowski problem in centroaffine geometry
• The centro-affine Minkowski problem for polytopes
• Geometry of log-concave functions and measures
• The Löwner function of a log-concave function
• Functional covering numbers
• Functional Versions ofL_p-Affine Surface Area and Entropy Inequalities
• Functional Inequalities related to the Rogers‐Shephard Inequality
• Logarithmically concave functions and sections of convex sets in $R^{n}$
• The Brunn-Minkowski inequality
• The Orlicz-Petty bodies
• On the $L_{p}$-Minkowski problem
• The logarithmic Minkowski problem
• On the general dual Orlicz-Minkowski problem
• Zhang’s Inequality for Log-Concave Functions
• Mixedf-divergence and inequalities for log-concave functions
• A note on Santaló inequality for the polarity transform and its reverse
• Logarithmically-Concave Moment Measures I
• The Lp Minkowski problem for polytopes for p<0
• Convex Bodies The Brunn-MinkowskiTheory
• The Santaló point of a function, and a functional form of the Santaló inequality
• $p$-Means of Convex Bodies.
• Convex Analysis