Emanuel Milman

activity

20242026

most citedFixed and Periodic Points of the Intersection Body Operator

1 citations · 1 across the 9 of their papers we have counts for

collaborators

10 papers

math.FA2026

Thin-Shell implies small-ball deviation via Gaussian tilts

Silouanos Brazitikos, Emanuel Milman

We show that uniform thin-shell estimates for isotropic log-concave measures $μ$ on $R^{n}$ yield precise and explicit deviation estimates for the Euclidean norm $∣ X ∣$ below…

math.SP2026

Spectral and Isoperimetric Bounds on Flat Tori

Emanuel Milman

We record several elementary relations between spectral and isoperimetric parameters of a flat torus $T_{Λ} = R^{n} /Λ$ and the covariance structure of a fundamental do…

math.FA2026

The Gaussian Conjugate Rogers-Shephard Inequality

Emanuel Milman, Shohei Nakamura, Hiroshi Tsuji

We fuse between the Rogers-Shephard inequality for the Lebesgue measure and Royen's Gaussian Correlation Inequality, simultaneously extending both into a single sharp inequality fo…

math.DG2025

On the connectedness of a minimizing cluster's boundary

Emanuel Milman, Joe Neeman

We verify that an isoperimetric minimizing cluster on a simply connected homogeneous Riemannian manifold with at most one end always has connected boundary. In particular, the boun…

math.DG2025

Multi-Bubble Isoperimetric Problems

Emanuel Milman

We survey recent advancements in the characterization of multi-bubble isoperimetric minimizers and the stability of soap bubble partitions. We conclude with some related open probl…

math.DG2025

Standard bubbles (and other Möbius-flat partitions) on model spaces are stable

Emanuel Milman, Botong Xu

We verify that for all $n \geq 3$ and $2 \leq k \leq n + 1$ , the standard $k$ -bubble clusters, conjectured to be minimizing total perimeter in $R^{n}$ , $S^{n}$ and $\ma…

math.FA2025

Gaussian Correlation via Inverse Brascamp-Lieb

Emanuel Milman

We give a simple alternative proof of Royen's Gaussian Correlation inequality by using (a slightly generalized version of) Nakamura-Tsuji's symmetric inverse Brascamp-Lieb inequali…

math.FA2024

A Blaschke-Santaló inequality for unconditional log-concave measures

Emanuel Milman, Amir Yehudayoff

The Blaschke-Santaló inequality states that the volume product $∣ K ∣ \cdot ∣ K^{o} ∣$ of a symmetric convex body $K \subset R^{n}$ is maximized by the standard Euclidean unit-b…

math.FA2024★ 1 cited

Fixed and Periodic Points of the Intersection Body Operator

Emanuel Milman, Shahar Shabelman, Amir Yehudayoff

The intersection body $I K$ of a star-body $K$ in $R^{n}$ was introduced by E. Lutwak following the work of H. Busemann, and plays a central role in the dual Brunn-Minkowski…

math.DG2024

Isoperimetric Inequalities on Slabs with applications to Cubes and Gaussian Slabs

Emanuel Milman

We study isoperimetric inequalities on "slabs", namely weighted Riemannian manifolds obtained as the product of the uniform measure on a finite length interval with a codimension-o…