DUAL CURVATURE MEASURES FOR LOG-CONCAVE FUNCTIONS

被引：1

作者：

Huang, Yong ^{[1
]}

Liu, Jiaqian ^{[1
,2
]}

Xi, Dongmeng ^{[3
]}

Zhao, Yiming ^{[4
]}

机构：

[1] Hunan Univ, Inst Math, 2 Lushan S Rd, Changsha 410082, Peoples R China

[2] Henan Univ, Sch Math & Stat, Kaifeng 475001, Peoples R China

[3] Shanghai Univ, Dept Math, 266 Jufengyuan Rd, Shanghai 200444, Peoples R China

[4] Syracuse Univ, Dept Math, 130 Sims Dr,215 Carnegie, Syracuse, NY 13244 USA

来源：

JOURNAL OF DIFFERENTIAL GEOMETRY | 2024年 / 128卷 / 02期

基金：

美国国家科学基金会; 中国国家自然科学基金;

关键词：

BUSEMANN-PETTY PROBLEM; MINKOWSKI-FIREY THEORY; SUBSPACE CONCENTRATION; AFFINE; INEQUALITIES; INTERIOR; SOBOLEV;

D O I：

10.4310/jdg/1727712894

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We introduce dual curvature measures for log-concave functions, which in the case of characteristic functions recover the dual curvature measures for convex bodies introduced by Huang-Lutwak-Yang-Zhang in 2016. Variational formulas are shown. The associated Minkowski problem for these dual curvature measures is considered and sufficient conditions in the symmetric setting are demonstrated.

引用

页码：815 / 860

页数：46

共 50 条

[41] Hypercontractivity for log-subharmonic functions [J].

Graczyk, Piotr ;

Kemp, Todd ;

Loeb, Jean-Jacques .

JOURNAL OF FUNCTIONAL ANALYSIS, 2010, 258 (06) :1785-1805

[42] Concave Continuations of Boolean Functions and Some of Their Properties and Applications [J].

Barotov, Dostonjon N. .

BULLETIN OF IRKUTSK STATE UNIVERSITY-SERIES MATHEMATICS, 2024, 49 :105-123

[43] Fractional smoothness of images of logarithmically concave measures under polynomials [J].

Kosov, Egor D. .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2018, 462 (01) :390-406

[44] On the Fekete-Szego problem for concave univalent functions [J].

Bhowmik, B. ;

Ponnusamy, S. ;

Wirths, K-J .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2011, 373 (02) :432-438

[45] Curvature measures and soap bubbles beyond convexity [J].

Hug, Daniel ;

Santilli, Mario .

ADVANCES IN MATHEMATICS, 2022, 411

[46] Bounded size biased couplings, log concave distributions and concentration of measure for occupancy models [J].

Bartroff, Jay ;

Goldstein, Larry ;

Islak, Umit .

BERNOULLI, 2018, 24 (4B) :3283-3317

[47] Best approximation of functions by log-polynomials [J].

Alonso-Gutierrez, David ;

Merino, Bernardo Gonzalez ;

Villa, Rafael .

JOURNAL OF FUNCTIONAL ANALYSIS, 2022, 282 (05)

[48] Concave Continuations of Boolean-like Functions and Some of Their Properties [J].

Barotov, Dostonjon N. .

BULLETIN OF IRKUTSK STATE UNIVERSITY-SERIES MATHEMATICS, 2025, 51 :82-100

[49] On Lp-Affine Surface Area and Curvature Measures [J].

Zhao, Yiming .

INTERNATIONAL MATHEMATICS RESEARCH NOTICES, 2016, 2016 (05) :1387-1423

[50] Prescribing Capacitary Curvature Measures on Planar Convex Domains [J].

Xiao, Jie .

JOURNAL OF GEOMETRIC ANALYSIS, 2020, 30 (02) :2225-2240

← 1 2 3 4 5 →