Emanuel Milman

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20242026

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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.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…