#### Filter Results:

- Full text PDF available (15)

#### Publication Year

2002

2014

- This year (0)
- Last 5 years (1)
- Last 10 years (13)

#### Publication Type

#### Co-author

#### Journals and Conferences

Learn More

- Emanuel Milman
- 2008

We show that for convex domains in Euclidean space, Cheeger’s isoperimetric inequality, spectral gap of the Neumann Laplacian, exponential concentration of Lipschitz functions, and the a-priori weakest requirement that Lipschitz functions have arbitrarily slow uniform tail-decay, are all quantitatively equivalent (to within universal constants, independent… (More)

- Emanuel Milman
- Games and Economic Behavior
- 2006

- Emanuel Milman
- 2009

It is well known that isoperimetric inequalities imply in a very general measuremetric-space setting appropriate concentration inequalities. The former bound the boundary measure of sets as a function of their measure, whereas the latter bound the measure of sets separated from sets having half the total measure, as a function of their mutual distance. We… (More)

- Emanuel Milman
- 2008

This is a continuation of our previous work [41]. It is well known that various isoperimetric inequalities imply their functional “counterparts”, but in general this is not an equivalence. We show that under certain convexity assumptions (e.g. for log-concave probability measures in Euclidean space), the latter implication can in fact be reversed for very… (More)

We prove an isoperimetric inequality for uniformly log-concave measures and for the uniform measure on a uniformly convex body. These inequalities imply the log-Sobolev inequalities proved by Bobkov and Ledoux [12] and Bobkov and Zegarlinski [13]. We also recover a concentration inequality for uniformly convex bodies, similar to that proved by Gromov and… (More)

- Emanuel Milman
- Math. Oper. Res.
- 2002

- Emanuel Milman
- 2007

In [Kol00], A. Koldobsky asked whether two types of generalizations of the notion of an intersection-body, are in fact equivalent. The structures of these two types of generalized intersection-bodies have been studied in [Mil06b], providing substantial evidence for a positive answer to this question. The purpose of this note is to construct a… (More)

- Emanuel Milman, Liran Rotem
- 2014

Elementary proofs of sharp isoperimetric inequalities on a normed space (R, ‖·‖) equipped with a measure μ = w(x)dx so that w is homogeneous are provided, along with a characterization of the corresponding equality cases. When p ∈ (0,∞] and in addition w is assumed concave, the result is an immediate corollary of the Borell–Brascamp–Lieb extension of the… (More)

- Emanuel Milman
- 2008

We study the structures of two types of generalizations of intersection-bodies and the problem of whether they are in fact equivalent. Intersection-bodies were introduced by Lutwak and played a key role in the solution of the Busemann-Petty problem. A natural geometric generalization of this problem considered by Zhang, led him to introduce one type of… (More)

- Emanuel Milman
- 2008

We develop a technique using dual mixed-volumes to study the isotropic constants of some classes of spaces. In particular, we recover, strengthen and generalize results of Ball and Junge concerning the isotropic constants of subspaces and quotients of Lp and related spaces. An extension of these results to negative values of p is also obtained, using… (More)