Stability of the Logarithmic Brunn-Minkowski Inequality in the Case of Many Hyperplane Symmetries

被引：0
作者：
Boroczky, Karoly J. [1 ]
De, Apratim [2 ]
机构：
[1] Alfred Renyi Inst Math, Realtanoda U 13-15, H-1053 Budapest, Hungary
[2] Cent European Univ, Dept Math, Nador U 9, H-1051 Budapest, Hungary
来源：
STUDIA SCIENTIARUM MATHEMATICARUM HUNGARICA | 2025年 / 61卷 / 04期
关键词：
Logarithmic Brunn-Minkowski conjecture; Brunn-Minkowski Inequality; Coxeter groups; stability; POLYA-SZEGO PRINCIPLE; GAUSS CURVATURE FLOW; CONE-VOLUME MEASURE; ISOPERIMETRIC INEQUALITY; FIREY THEORY; AFFINE; EXTENSIONS; CONJECTURE; ENTROPY; VERSION;
D O I：
10.1556/012.2024.04321
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In the case of symmetries with respect to n independent linear hyperplanes, a stability versions of the Logarithmic Brunn-Minkowski Inequality and the Logarithmic Minkowski Inequality for convex bodies are established.
引用
收藏
页码：341 / 376
页数：36
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共 96 条
  • [1] Adams J.F., Lectures on exceptional Lie groups, Chicago Lectures in Mathematics, (1996)
  • [2] Andrews B., Gauss curvature flow: the fate of the rolling stones, Invent. Math., 138, 1, pp. 151-161, (1999)
  • [3] Artstein-Avidan S., Florentin D.I., Segal A., Functional Brunn–Minkowski inequalities induced by polarity, Adv. Math., 364
  • [4] Ball K.M., (1988)
  • [5] Barthe F., Autour de l’inégalité de Brunn–Minkowski, mémoire d’habilitation, (2008)
  • [6] Barthe F., Cordero-Erausquin D., Invariances in variance estimates, Proc. Lond. Math. Soc., 106, 1, pp. 33-64, (2013)
  • [7] Barthe F., Fradelizi M., The volume product of convex bodies with many hyperplane symmetries, Amer. J. Math., 135, 2, pp. 311-347, (2013)
  • [8] Barthe F., Guedon O., Mendelson Sh., Naor A., A probabilistic approach to the geometry of the l<sub>p</sub><sup>n</sup>-ball, Ann. Probab., 33, 2, pp. 480-513, (2005)
  • [9] Bianchi G., Egnell H., A note on the Sobolev inequality, J. Funct. Anal., 100, 1, pp. 18-24, (1991)
  • [10] Bollobas B., Leader I., Products of unconditional bodies, Geometric aspects of functional analysis (Israel, 1992–1994), volume 77 of Oper. Theory Adv. Appl., pp. 13-24, (1995)
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