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积分几何不变运动公式与弦幂积分不等式
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作者 徐文学 周家足 《中国科学:数学》 CSCD 北大核心 2024年第10期1707-1722,共16页
本文先介绍积分几何与凸几何的历史、发展、研究现状和中国学者的一些工作.然后介绍我们在不变运动公式和弦幂积分不等式方面的一些最新工作,还介绍与积分几何密切相关的凸体类上的仿射等周不等式.
关键词 不变运动公式 等周不等式 BONNESEN型不等式 仿射等周不等式 弦幂积分
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Projection Body and Isoperimetric Inequalities for s-Concave Functions
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作者 Niufa FANG jiazu zhou 《Chinese Annals of Mathematics,Series B》 SCIE CSCD 2023年第3期465-480,共16页
For a positive integer s,the projection body of an s-concave function f:R^(n)→[0,+∞),a convex body in the(n+s)-dimensional Euclidean space R^(n+s),is introduced.Associated inequalities for s-concave functions,such a... For a positive integer s,the projection body of an s-concave function f:R^(n)→[0,+∞),a convex body in the(n+s)-dimensional Euclidean space R^(n+s),is introduced.Associated inequalities for s-concave functions,such as,the functional isoperimetric inequality,the functional Petty projection inequality and the functional Loomis-Whitney inequality are obtained. 展开更多
关键词 Isoperimetric inequality s-Concave functions Projection body The Petty projection inequality
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Continuity of the solution to the even logarithmic Minkowski problem in the plane 被引量:3
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作者 Hejun Wang Niufa Fang jiazu zhou 《Science China Mathematics》 SCIE CSCD 2019年第7期1419-1428,共10页
This paper investigates continuity of the solution to the even logarithmic Minkowski problem in the plane. It is shown that the weak convergence of a sequence of cone-volume measures in R^2 implies the convergence of ... This paper investigates continuity of the solution to the even logarithmic Minkowski problem in the plane. It is shown that the weak convergence of a sequence of cone-volume measures in R^2 implies the convergence of the sequence of the corresponding origin-symmetric convex bodies in the Hausdorff metric. 展开更多
关键词 CONVEX body cone-volume measure logarithmic MINKOWSKI problem
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(p,q)-John椭球
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作者 李晓 王贺军 周家足 《中国科学:数学》 CSCD 北大核心 2021年第2期343-364,共22页
本文主要研究(p,q)-John椭球.经典的John椭球和L_(p) John椭球均是(p,q)-John椭球的特殊情形.首先讨论(p,q)-John椭球的充分必要条件和连续性.得到了关于(p,q)-John椭球的不等式和包含关系,所得到的不等式和包含关系分别类似于Ball体积... 本文主要研究(p,q)-John椭球.经典的John椭球和L_(p) John椭球均是(p,q)-John椭球的特殊情形.首先讨论(p,q)-John椭球的充分必要条件和连续性.得到了关于(p,q)-John椭球的不等式和包含关系,所得到的不等式和包含关系分别类似于Ball体积比不等式和John包含关系. 展开更多
关键词 (p q)-John椭球 体积比不等式 John包含关系
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The LYZ centroid conjecture for star bodies 被引量:2
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作者 Denghui Wu jiazu zhou 《Science China Mathematics》 SCIE CSCD 2018年第7期1273-1286,共14页
Lutwak et al.(2010) established the Orlicz centroid inequality for convex bodies and conjectured that their Orlicz centroid inequality could be extended to star bodies. Zhu(2012) confirmed the conjectured Lutwak, Yang... Lutwak et al.(2010) established the Orlicz centroid inequality for convex bodies and conjectured that their Orlicz centroid inequality could be extended to star bodies. Zhu(2012) confirmed the conjectured Lutwak, Yang and Zhang(LYZ) Orlicz centroid inequality and solved the equality condition for the case that φis strictly convex. Without the condition that φ is strictly convex, this paper studies the equality condition of the conjectured LYZ Orlicz centroid inequality for star bodies. 展开更多
关键词 Brunn-Minkowski theory Orlicz centroid body Orlicz centroid inequality star body Steiner symmetrization
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The Busemann-Petty problem on entropy of log-concave functions 被引量:2
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作者 Niufa Fang jiazu zhou 《Science China Mathematics》 SCIE CSCD 2022年第10期2171-2182,共12页
The Busemann-Petty problem asks whether symmetric convex bodies in the Euclidean space R^(n) with smaller central hyperplane sections necessarily have smaller volumes.The solution has been completed and the answer is ... The Busemann-Petty problem asks whether symmetric convex bodies in the Euclidean space R^(n) with smaller central hyperplane sections necessarily have smaller volumes.The solution has been completed and the answer is affirmative if n≤4 and negative if n≥5.In this paper,we investigate the Busemann-Petty problem on entropy of log-concave functions:for even log-concave functions f and g with finite positive integrals in R^(n),if the marginal∫_(R^(n))∩H^(f(x)dx)of f is smaller than the marginal∫_(R^(n))∩H^(g(x)dx)of g for every hyperplane H passing through the origin,is the entropy Ent(f)of f bigger than the entropy Ent(g)of g?The BusemannPetty problem on entropy of log-concave functions includes the Busemann-Petty problem,and hence its answer is negative when n≥5.For 2≤n≤4,we give a positive answer to the Busemann-Petty problem on entropy of log-concave functions. 展开更多
关键词 Busemann-Petty problem ENTROPY intersection functions log-concave functions
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Kinematic Formulas of Total Mean Curvatures for Hypersurfaces
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作者 Ming LI jiazu zhou 《Chinese Annals of Mathematics,Series B》 SCIE CSCD 2016年第1期137-148,共12页
kinematic Euclidean By using the moving frame method, the authors obtain a kind of asymmetric formulas for the total mean curvatures of hypersurfaces in the n-dimensional space
关键词 Kinematic formula Total mean curvature HYPERSURFACE
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