60 citations · 342 across the 44 of their papers we have counts for
28 papers · 1 filter
Centro-Affine Differential Geometry and the Log-Minkowski Problem
Emanuel Milman
We interpret the log-Brunn-Minkowski conjecture of Böröczky-Lutwak-Yang-Zhang as a spectral problem in centro-affine differential geometry. In particular, we show that the Hilbert-…
A sharp centro-affine isospectral inequality of Szegö--Weinberger type and the -Minkowski problem
Emanuel Milman
We establish a sharp upper-bound for the first non-zero even eigenvalue (corresponding to an even eigenfunction) of the Hilbert-Brunn-Minkowski operator associated to a strongly co…
Reverse Hölder Inequalities for log-Lipschitz Functions
Emanuel Milman
Reverse Hölder inequalities for a class of functions on a probability space constitute an important tool in Analysis in Probability. After revisiting how a (modified) log-Sobolev i…
Regular Random Sections of Convex Bodies and the Random Quotient-of-Subspace Theorem
Emanuel Milman, Yuval Yifrach
It was shown by G. Pisier that any finite-dimensional normed space admits an -regular -position, guaranteeing not only regular entropy estimates but moreover regular estimate…
The Quasi Curvature-Dimension Condition with applications to sub-Riemannian manifolds
Emanuel Milman
We obtain the best known quantitative estimates for the -Poincaré and log-Sobolev inequalities on domains in various sub-Riemannian manifolds, including ideal Carnot groups an…
The Gaussian Double-Bubble Conjecture
Emanuel Milman, Joe Neeman
We establish the Gaussian Double-Bubble Conjecture: the least Gaussian-weighted perimeter way to decompose into three cells of prescribed (positive) Gaussian measure…