Convex geometry and its connections to harmonic analysis, functional analysis and probability theory

DOI10.4171/icm2022/65OpenAlexW4389775307MaRDI QIDQ6119188

Publication date: 22 March 2024

Published in: International Congress of Mathematicians (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.4171/icm2022/65

zbMATH Keywords

probability isoperimetric inequality harmonic analysis central limit theorem optimal transport convex geometry

Mathematics Subject Classification ID

Central limit and other weak theorems (60F05) Local theory of Banach spaces (46B07) Harmonic analysis in several variables (42B99) Convexity and finite-dimensional Banach spaces (including special norms, zonoids, etc.) (aspects of convex geometry) (52A21) Convex sets in (n) dimensions (including convex hypersurfaces) (52A20)

Cites Work

Properties of Conformal Invariants
The Slicing Problem by Bourgain
Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
The isotropic position and the reverse Santaló inequality
Approaching the Kannan-Lovász-Simonovits and variance conjectures
Interpolating thin-shell and sharp large-deviation estimates for isotropic log-concave measures
Regularity of Gaussian processes
Contributions to the theory of convex bodies
An optimal Poincaré inequality for convex domains
Gaussian kernels have only Gaussian maximizers
Restricted chord projection and affine inequalities
Concentration of mass on convex bodies
On convex perturbations with a bounded isotropic constant
Power-law estimates for the central limit theorem for convex sets
The quantitative isoperimetric inequality and related topics
Increasing functions and inverse Santaló inequality for unconditional functions
Concentration in a thin Euclidean shell for log-concave measures
A mass transportation approach to quantitative isoperimetric inequalities
On the role of convexity in isoperimetry, spectral gap and concentration
From the Mahler conjecture to Gauss linking integrals
General \(L_{p}\) affine isoperimetric inequalities
Asymptotic theory of finite dimensional normed spaces. With an appendix by M. Gromov: Isoperimetric inequalities in Riemannian manifolds
Intersection bodies and dual mixed volumes
Bounded orthogonal systems and the \(\Lambda\) (p)-set problem
The Brunn-Minkowski inequality in Gauss space
On extensions of the Brunn-Minkowski and Prekopa-Leindler theorems, including inequalities for log concave functions, and with an application to the diffusion equation
Best constants in Young's inequality, its converse, and its generalization to more than three functions
Inequalities in Fourier analysis
Best constant in Sobolev inequality
Problèmes isoperimetriques et espaces de Sobolev
The dimension of almost spherical sections of convex bodies
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
Best constants for Gagliardo-Nirenberg inequalities and applications to nonlinear diffusions.
Entropy jumps in the presence of a spectral gap
A mass-transportation approach to sharp Sobolev and Gagliardo-Nirenberg inequalities.
Isoperimetric and analytic inequalities for log-concave probability measures
Asymptotics of cross sections for convex bodies
\(L_ p\) affine isoperimetric inequalities.
New volume ratio properties for convex symmetric bodies in \({\mathbb{R}}^ n\)
A positive answer to the Busemann-Petty problem in three dimensions
A sharp analog of Young's inequality on \(S^N\) and related entropy inequalities
Isoperimetric problems for convex bodies and a localization lemma
A functional form of the isoperimetric inequality for the Gaussian measure
On the second differentiability of convex surfaces
Existence and uniqueness of monotone measure-preserving maps
Asymptotics of graphical projection pursuit
Quantitative stability for sumsets in \(\mathbb R^n\)
Thin shell implies spectral gap up to polylog via a stochastic localization scheme
A stability result for mean width of \(L_{p}\)-centroid bodies
The sharp quantitative isoperimetric inequality
A central limit theorem for convex sets
The Brascamp-Lieb inequalities: Finiteness, structure and extremals
On the Blaschke-Santaló inequality
Über einige Affinvarianten konvexer Bereiche
Approximately gaussian marginals and the hyperplane conjecture
Problems on convex bodies
Surface Area of a Convex Body Under Affine Transformations
Volume Ratios and a Reverse Isoperimetric Inequality
Some methods for studying stability in isoperimetric type problems
A Topological Application of the Isoperimetric Inequality
Cube Slicing in R n
Slicing Convex Bodies-Bounds for Slice Area in Terms of the Body's Covariance
Polar factorization and monotone rearrangement of vector‐valued functions
The Regularity of Mappings with a Convex Potential
A quantitative isoperimetric inequality in n-dimensional space.
Logarithmic Sobolev Inequalities
The existence of a centrally symmetric convex body with central sections that are unexpectedly small
A random polynomial-time algorithm for approximating the volume of convex bodies
Inégalités de Brascamp-Lieb et convexité
The central limit problem for convex bodies
Isotropic surface area measures
Stability in the Isoperimetric Problem for Convex or Nearly Spherical Domains in R n
Solution of Shannon’s problem on the monotonicity of entropy
Entropy jumps for isotropic log-concave random vectors and spectral gap
The Hörmander Proof of the Bourgain–Milman Theorem
The Kannan–Lovász–Simonovits conjecture
Bounding the Norm of a Log-Concave Vector Via Thin-Shell Estimates
Asymptotic Geometric Analysis, Part I
A Theorem on Convex Bodies of the Brunn-Minkowski Type