Zobrazeno 1 - 10
of 188
pro vyhledávání: '"Milman, Emanuel"'
Autor:
Milman, Emanuel, Yehudayoff, Amir
The Blaschke-Santal\'o inequality states that the volume product $|K| \cdot |K^o|$ of a symmetric convex body $K \subset \mathbb{R}^n$ is maximized by the standard Euclidean unit-ball. Cordero-Erausquin asked whether the inequality remains true for a
Externí odkaz:
http://arxiv.org/abs/2410.21093
The intersection body $IK$ of a star-body $K$ in $\mathbb{R}^n$ was introduced by E. Lutwak following the work of H. Busemann, and plays a central role in the dual Brunn-Minkowski theory. We show that when $n \geq 3$, $I^2 K = c K$ iff $K$ is a cente
Externí odkaz:
http://arxiv.org/abs/2408.08171
Autor:
Milman, Emanuel
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-one base. As our two main applications, we consider the case when the b
Externí odkaz:
http://arxiv.org/abs/2403.06602
Autor:
Ivaki, Mohammad N., Milman, Emanuel
Let $K$ be a smooth, origin-symmetric, strictly convex body in $\mathbb{R}^n$. If for some $\ell\in GL(n,\mathbb{R})$, the anisotropic Riemannian metric $\frac{1}{2}D^2 \Vert\cdot\Vert_{\ell K}^2$, encapsulating the curvature of $\ell K$, is comparab
Externí odkaz:
http://arxiv.org/abs/2307.16484
Autor:
Milman, Emanuel, Neeman, Joe
The multi-bubble isoperimetric conjectures in $n$-dimensional Euclidean and spherical spaces from the 1990's assert that standard bubbles uniquely minimize total perimeter among all $q-1$ bubbles enclosing prescribed volume, for any $q \leq n+2$. The
Externí odkaz:
http://arxiv.org/abs/2307.08164
Autor:
Ivaki, Mohammad N., Milman, Emanuel
Employing a local version of the Brunn-Minkowski inequality, we give a new and simple proof of a result due to Andrews, Choi and Daskalopoulos that the origin-centred balls are the only closed, self-similar solutions of the Gauss curvature flow. Exte
Externí odkaz:
http://arxiv.org/abs/2304.12839
Autor:
Milman, Emanuel, Neeman, Joe
The multi-bubble isoperimetric conjecture in $n$-dimensional Euclidean and spherical spaces from the 1990's asserts that standard bubbles uniquely minimize total perimeter among all $q-1$ bubbles enclosing prescribed volume, for any $q \leq n+2$. The
Externí odkaz:
http://arxiv.org/abs/2205.09102
Autor:
Milman, Emanuel
We interpret the log-Brunn-Minkowski conjecture of B\"or\"oczky-Lutwak-Yang-Zhang as a spectral problem in centro-affine differential geometry. In particular, we show that the Hilbert-Brunn-Minkowski operator coincides with the centro-affine Laplacia
Externí odkaz:
http://arxiv.org/abs/2104.12408
Autor:
Milman, Emanuel
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 convex $C^2$-smooth origin-symmetric convex body $K$ in $\mathbb{R}^n$.
Externí odkaz:
http://arxiv.org/abs/2103.02994