Dual curvature measures for \(\log\)-concave functions

DOI10.4310/jdg/1727712894MaRDI QIDQ6633910

Jiaqian Liu, Yong Huang, Yiming Zhao, Dongmeng Xi

Publication date: 6 November 2024

Published in: Journal of Differential Geometry (Search for Journal in Brave)

Mathematics Subject Classification ID

Inequalities and extremum problems involving convexity in convex geometry (52A40) Length, area, volume and convex sets (aspects of convex geometry) (52A38) Variational methods for second-order elliptic equations (35J20)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Sharp stability theorems for the anisotropic Sobolev and log-Sobolev inequalities on functions of bounded variation
• Operations between sets in geometry
• Real Monge-Ampère equations and Kähler-Ricci solitons on toric log Fano varieties
• Functional affine-isoperimetry and an inverse logarithmic Sobolev inequality
• The log-Brunn-Minkowski inequality
• \(\mathrm{SL}(n)\) invariant valuations on polytopes
• Minkowski areas and valuations
• Interior a priori estimates for solutions of fully nonlinear equations
• The Brunn-Minkowski-Firey theory. I: Mixed volumes and the Minkowski problem
• Minkowski valuations intertwining the special linear group
• Geometric measures in the dual Brunn-Minkowski theory and their associated Minkowski problems
• Affine isoperimetric inequalities in the functional Orlicz-Brunn-Minkowski theory
• Functions of bounded variation on ``good metric spaces
• Interior \(W^{2,p}\) estimates for solutions of the Monge-Ampère equation
• A localization property of viscosity solutions to the Monge-Ampère equation and their strict convexity
• Crofton measures and Minkowski valuations
• A mass transportation approach to quantitative isoperimetric inequalities
• A characterization of the duality mapping for convex bodies
• Intersection bodies and dual mixed volumes
• A positive solution to the Busemann-Petty problem in \(\mathbb{R}^4\)
• An analytic solution to the Busemann-Petty problem on sections of convex bodies
• Ellipsoids and matrix-valued valuations
• Volumen und Oberfläche.
• Existence of solutions to the even dual Minkowski problem
• General volumes in the Orlicz-Brunn-Minkowski theory and a related Minkowski problem. I
• On the \(L_p\) dual Minkowski problem
• On the planar dual Minkowski problem
• Subspace concentration of dual curvature measures of symmetric convex bodies
• Necessary subspace concentration conditions for the even dual Minkowski problem
• The \(L_{p}\) dual Minkowski problem for \(p\) 1 and \(q\) 0
• \(L_{p}\) dual curvature measures
• A positive answer to the Busemann-Petty problem in three dimensions
• The Brunn-Minkowski-Firey theory. II: Affine and geominimal surface areas
• The Minkowski problem in Gaussian probability space
• Variations of a class of Monge-Ampère-type functionals and their applications
• The \(L_p\) dual Minkowski problem and related parabolic flows
• Surface area measures of log-concave functions
• Geometry of log-concave functions: the \(L_p\) Asplund sum and the \(L_p\) Minkowski problem
• The Hadwiger theorem on convex functions. III: Steiner formulas and mixed Monge-Ampère measures
• The \(L_p\)-Brunn-Minkowski inequality for \(p<1\)
• Flow by Gauss curvature to the Aleksandrov and dual Minkowski problems
• Moment measures
• The concept of duality in convex analysis, and the characterization of the Legendre transform
• Affine Orlicz Pólya-Szegő principle for log-concave functions
• Smooth solutions to the \(L_p\) dual Minkowski problem
• Quermassintegrals of quasi-concave functions and generalized Prékopa-Leindler inequalities
• The first variation of the total mass of log-concave functions and related inequalities
• On the \(L_{p}\) Minkowski problem for polytopes
• The \(L_p\)-Minkowski problem and the Minkowski problem in centroaffine geometry
• The Hadwiger theorem on convex functions. IV: The Klain approach
• The Centro-Affine Hadwiger Theorem
• A flow method for the dual Orlicz–Minkowski problem
• Hessian valuations
• On the regularity of the solution of then-dimensional Minkowski problem
• Variational Analysis
• The Brunn-Minkowski inequality
• The logarithmic Minkowski problem
• Local 𝐿^{𝑝}-Brunn–Minkowski inequalities for 𝑝<1
• Mixedf-divergence and inequalities for log-concave functions
• Convex Bodies The Brunn-MinkowskiTheory
• The Santaló point of a function, and a functional form of the Santaló inequality

Related Items (1)

Dual Orlicz curvature measures for log-concave functions and their Minkowski problems

This page was built for publication: Dual curvature measures for \(\log\)-concave functions