Weighted Minkowski’s existence theorem and projection bodies

DOI10.1090/tran/8992zbMath1527.52007arXiv2111.10923OpenAlexW4379618804MaRDI QIDQ6062119

Publication date: 30 November 2023

Full work available at URL: https://arxiv.org/abs/2111.10923

projection body Shephard problem petty projection inequality Ehrhard's inequality Minkowski's existence theorem

Existence theories for free problems in two or more independent variables (49J10) Inequalities and extremum problems involving convexity in convex geometry (52A40) Mixed volumes and related topics in convex geometry (52A39) Convexity and finite-dimensional Banach spaces (including special norms, zonoids, etc.) (aspects of convex geometry) (52A21)

Cites Work

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Generic mean curvature flow. I: Generic singularities
A hyperplane inequality for measures of convex bodies in $\mathbb R^{n }, \; n\leq 4$
The log-Brunn-Minkowski inequality
An example related to the slicing inequality for general measures
The Brunn-Minkowski-Firey theory. I: Mixed volumes and the Minkowski problem
Geometric measures in the dual Brunn-Minkowski theory and their associated Minkowski problems
The hyperplane is the only stable, smooth solution to the isoperimetric problem in Gaussian space
The difference body of a convex body
Restricted chord projection and affine inequalities
The Hadamard variational formula and the Minkowski problem for $p$-capacity
Gaussian measure of sections of dilates and translations of convex bodies
Orlicz centroid bodies
The even Orlicz Minkowski problem
General $L_{p}$ affine isoperimetric inequalities
Orlicz projection bodies
Éléments extrémaux pour les inégalités de Brunn-Minkowski gaussiennes (Extreme elements for the Gaussian Brunn-Minkowski inequalities)
Intersection bodies and dual mixed volumes
On the Busemann-Petty problem for perturbations of the ball
Convex set functions in d-space
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
An analytic solution to the Busemann-Petty problem on sections of convex bodies
The reverse isoperimetric problem for Gaussian measure
The Ehrhard inequality
The Brunn-Minkowski inequality for $p$-capacity of convex bodies
$L_ p$ affine isoperimetric inequalities.
The Busemann-Petty problem for arbitrary measures
Intersection bodies and the Busemann-Petty inequalities in $\mathbb{R}^ 4$
Projections of convex bodies and the Fourier transform
On the case of equality in the Brunn-Minkowski inequality for capacity
The Brunn-Minkowski-Firey theory. II: Affine and geominimal surface areas
The Minkowski problem in Gaussian probability space
On the $L_p$-Brunn-Minkowski and dimensional Brunn-Minkowski conjectures for log-concave measures
The $L_p$-Gaussian Minkowski problem
The dimensional Brunn-Minkowski inequality in Gauss space
On the Gardner-Zvavitch conjecture: symmetry in inequalities of Brunn-Minkowski type
Complemented Brunn-Minkowski inequalities and isoperimetry for homogeneous and non-homogeneous measures
An isomorphic version of the Busemann-Petty problem for arbitrary measures
Rogers-Shephard type inequalities for sections
An extension of Minkowski's theorem and its applications to questions about projections for measures
Wulff shapes and a characterization of simplices via a Bezout type inequality
On the stability of Brunn-Minkowski type inequalities
A generalization of $L_{p}$-Brunn-Minkowski inequalities and $L_{p}$-Minkowski problems for measures
Asymmetric affine $L_p$ Sobolev inequalities
Shadow systems of convex sets
A $\sqrt{n}$ estimate for measures of hyperplane sections of convex bodies
The $L_p$-Minkowski problem and the Minkowski problem in centroaffine geometry
Slicing inequalities for measures of convex bodies
Zu einem Problem von Shephard über die Projektionen konvexer Körper
The direct method in the calculus of variations for convex bodies
A note on a Brunn-Minkowski inequality for the Gaussian measure
Gaussian Brunn-Minkowski inequalities
Problems on convex bodies
Symétrisation dans l'espace de Gauss.
A note on a problem of H. Busemann and C. M. Petty concerning sections of symmetric convex bodies
Shadows of Convex Bodies
On the Busemann‐Petty problem about convex, centrally symmetric bodies in
The existence of a centrally symmetric convex body with central sections that are unexpectedly small
Finite dimensional subspaces of $L_{p}$
An analytic solution to the Busemann-Petty problem
Intersection Bodies and the Busemann-Petty Problem
A note on the Ehrhard inequality
The logarithmic Minkowski problem
Poincaré and Brunn-Minkowski inequalities on the boundary of weighted Riemannian manifolds
On $L_p$-Brunn-Minkowski type and $L_p$-isoperimetric type inequalities for measures
On the Comparison of Measures of Convex Bodies via Projections and Sections
Measure comparison and distance inequalities for convex bodies
The Lower Bound for Koldobsky’s Slicing Inequality via Random Rounding
Asymptotic Geometric Analysis, Part I
Convex Bodies The Brunn-MinkowskiTheory
Minkowski valuations
Optimal Sobolev norms and the Lp Minkowski problem
$p$-Means of Convex Bodies.
Weighted Brunn-Minkowski theory. I: On weighted surface area measures
General measure extensions of projection bodies

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