DUAL CURVATURE MEASURES FOR LOG-CONCAVE FUNCTIONS

被引：0
|
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：
中国国家自然科学基金; 美国国家科学基金会;
关键词：
BUSEMANN-PETTY PROBLEM; MINKOWSKI-FIREY THEORY; SUBSPACE CONCENTRATION; AFFINE; INEQUALITIES; INTERIOR; SOBOLEV;
D O I：
暂无
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
收藏
页码：815 / 860
页数：46
相关论文
共 50 条
  • [1] Dual Orlicz curvature measures for log-concave functions and their Minkowski problems
    Fang, Niufa
    Ye, Deping
    Zhang, Zengle
    Zhao, Yiming
    CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, 2025, 64 (02)
  • [2] Geometry of Log-concave Functions and Measures
    B. Klartag
    V. D. Milman
    Geometriae Dedicata, 2005, 112 : 169 - 182
  • [3] Geometry of log-concave functions and measures
    Klartag, B
    Milman, V
    GEOMETRIAE DEDICATA, 2005, 112 (01) : 169 - 182
  • [4] Surface area measures of log-concave functions
    Liran Rotem
    Journal d'Analyse Mathématique, 2022, 147 : 373 - 400
  • [5] Surface area measures of log-concave functions
    Rotem, Liran
    JOURNAL D ANALYSE MATHEMATIQUE, 2022, 147 (01): : 373 - 400
  • [6] LOG-CONCAVE MEASURES
    Feyel, D.
    Uestuenel, A. S.
    TWMS JOURNAL OF PURE AND APPLIED MATHEMATICS, 2010, 1 (01): : 92 - 105
  • [7] Log-Concave Functions
    Colesanti, Andrea
    CONVEXITY AND CONCENTRATION, 2017, 161 : 487 - 524
  • [8] Valuations on Concave Functions and Log-Concave Functions
    LIU Lijuan
    Wuhan University Journal of Natural Sciences, 2019, 24 (06) : 479 - 484
  • [9] Valuations on Log-Concave Functions
    Mussnig, Fabian
    JOURNAL OF GEOMETRIC ANALYSIS, 2021, 31 (06) : 6427 - 6451
  • [10] On the MeanWidth of Log-Concave Functions
    Rotem, Liran
    GEOMETRIC ASPECTS OF FUNCTIONAL ANALYSIS: ISRAEL SEMINAR 2006-2010, 2012, 2050 : 355 - 372
12345