3 citations · 11 across the 11 of their papers we have counts for
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Functional perimeter and the dimensional Brunn-Minkowski inequality for log-concave measures
Alexandros Eskenazis, Apostolos Giannopoulos, Natalia Tziotziou
This paper is dedicated to two geometric problems associated to log-concave measures on . First, we study the dimensional Brunn-Minkowski inequality for even log-conc…
Some geometric applications of the discrete heat flow
Alexandros Eskenazis
We present two geometric applications of heat flow methods on the discrete hypercube . First, we prove that if is a finite-dimensional normed space, then the bi-Lip…
Average distortion embeddings, nonlinear spectral gaps, and a metric John theorem (after Assaf Naor)
Alexandros Eskenazis
We survey various aspects of the theory of nonlinear spectral gaps. In particular, we present a self-contained proof of Naor's average John theorem.
The dimensional Brunn-Minkowski inequality in Gauss space
Alexandros Eskenazis, Georgios Moschidis
Let be the standard Gaussian measure on . We prove that for every symmetric convex sets in and every , $$γ_n(λK+(1-λ)L)^{\frac{1…
Nonpositive curvature is not coarsely universal
Alexandros Eskenazis, Manor Mendel, Assaf Naor
We prove that not every metric space embeds coarsely into an Alexandrov space of nonpositive curvature. This answers a question of Gromov (1993) and is in contrast to the fact that…
On extremal sections of subspaces of
Alexandros Eskenazis
Let and . For a finite dimensional quasi-normed space , let $$B_p^n(X) = \Big\{ (x_1,\ldots,x_n)\in\big(\mathbb{R}…