Projective Transformations of Convex Bodies and Volume Product

被引：0

作者：

Balacheff, Florent ^{[1
]}

Solanes, Gil ^{[1
,2
]}

Tzanev, Kroum ^{[3
]}

机构：

[1] Univ Autonoma Barcelona, Dept Matemat, Barcelona 08193, Spain

[2] Ctr Recerca Matemat, Barcelona 08193, Spain

[3] Univ Lille, Lab Paul Painleve, F-59650 Villeneuve DAscq, France

来源：

INTERNATIONAL MATHEMATICS RESEARCH NOTICES | 2024年 / 2024卷 / 11期

关键词：

D O I：

10.1093/imrn/rnad310

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we study certain variational aspects of the volume product functional restricted to the space of small projective deformations of a fixed convex body. In doing so, we provide a short proof of a theorem by Klartag: a strong version of the slicing conjecture implies the non-symmetric Mahler conjecture. We also exhibit an interesting family of critical convex bodies in dimension $2$ containing saddle points for this functional.

引用

页码：9054 / 9065

页数：12