THE VOLUME PRODUCT OF CONVEX BODIES WITH MANY HYPERPLANE SYMMETRIES

被引：0

作者：

Barthe, F. ^{[1
]}

Fradelizi, M. ^{[2
]}

机构：

[1] Univ Toulouse 3, Equipe Stat & Probabil, CNRS, IMT,UMR 5219, F-31062 Toulouse 9, France

[2] Univ Paris Est Marne La Vallee, Lab Anal & Math Appl, UMR 8050, F-77454 Marne La Vallee 2, France

来源：

AMERICAN JOURNAL OF MATHEMATICS | 2013年 / 135卷 / 02期

关键词：

SANTALO INEQUALITY; MAHLER CONJECTURE; LOCAL MINIMALITY; INTEGRALS; ZONOIDS; SPACES;

D O I：

暂无

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Mahler's conjecture predicts a sharp lower bound on the volume of the polar of a convex body in terms of its volume. We confirm the conjecture for convex bodies with many hyperplane symmetries in the following sense: their hyperplanes of symmetries have a one-point intersection. Moreover, we obtain improved sharp lower bounds for classes of convex bodies which are invariant by certain reflection groups, namely direct products of the isometry groups of regular polytopes.

引用

页码：311 / 347

页数：37

共 42 条

[31] Many-valued convex structures induced by fuzzy inclusion orders
Wang, Kai
Shi, Fu-Gui
JOURNAL OF INTELLIGENT & FUZZY SYSTEMS, 2019, 36 (04) : 3373 - 3383
[32] Sections of Convex Bodies in John's and Minimal Surface Area Position
Alonso-Gutierrez, David
Brazitikos, Silouanos
INTERNATIONAL MATHEMATICS RESEARCH NOTICES, 2023, 2023 (01) : 243 - 297
[33] SYMMETRIC MAHLER'S CONJECTURE FOR THE VOLUME PRODUCT IN THE 3-DIMENSIONAL CASE
Iriyeh, Hiroshi
Shibata, Masataka
DUKE MATHEMATICAL JOURNAL, 2020, 169 (06) : 1077 - 1134
[34] Diameter, width and thickness of spherical reduced convex bodies with an application to Wulff shapes
Lassak, Marek
BEITRAGE ZUR ALGEBRA UND GEOMETRIE-CONTRIBUTIONS TO ALGEBRA AND GEOMETRY, 2020, 61 (02): : 369 - 379
[35] LR Characterization of Chirotopes of Finite Planar Families of Pairwise Disjoint Convex bodies
Habert, Luc
Pocchiola, Michel
DISCRETE & COMPUTATIONAL GEOMETRY, 2013, 50 (03) : 552 - 648
[36] Regular random sections of convex bodies and the random Quotient-of-Subspace Theorem
Milman, Emanuel
Yifrach, Yuval
JOURNAL OF FUNCTIONAL ANALYSIS, 2021, 281 (07)
[37] ORIGIN-SYMMETRIC BODIES OF REVOLUTION WITH MINIMAL MAHLER VOLUME IN R3-A NEW PROOF
Lin, Youjiang
Leng, Gangsong
JOURNAL OF MATHEMATICAL INEQUALITIES, 2014, 8 (03): : 375 - 404
[38] Convex MV-Algebras: Many-Valued Logics Meet Decision Theory
Flaminio, T.
Hosni, H.
Lapenta, S.
STUDIA LOGICA, 2018, 106 (05) : 913 - 945
[39] Variants of Hormander's theorem on q-convex manifolds by a technique of infinitely many weights
Ohsawa, Takeo
ABHANDLUNGEN AUS DEM MATHEMATISCHEN SEMINAR DER UNIVERSITAT HAMBURG, 2021, 91 (01): : 81 - 99
[40] Many-body topological invariants in fermionic symmetry-protected topological phases: Cases of point group symmetries
Shiozaki, Ken
Shapourian, Hassan
Ryu, Shinsei
PHYSICAL REVIEW B, 2017, 95 (20)

← 1 2 3 4 5 →