Mixed Volumes and Measures of Asymmetry

The mixed volume and the measure of asymmetry for convex bodies are two important topics in convex geometry.In this paper,we first reveal a close connection between the Lp-mixed volumes proposed by E.Lutwak and the p-measures of asymmetry,which have the Minkowski measure as a special case,introduced...

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Bibliographic Details
Published inActa mathematica Sinica. English series Vol. 30; no. 11; pp. 1905 - 1916
Main Authors Jin, Hai Lin, Leng, Gang Song, Guo, Qi
Format Journal Article
LanguageEnglish
Published Heidelberg Institute of Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society 01.11.2014
Springer Nature B.V
Subjects
Asymmetry
Euclidean space
Geometry
Joints
Mathematical models
Mathematicians
Mathematics
Mathematics and Statistics
Studies
Symmetry
Theorems
不对称
几何
凸体
混合体积
脂蛋白
52A20
Orlicz mixed volume
measure of asymmetry
Orlicz measure of asymmetry
52A39
Minkowski measure of asymmetry
mixed volume
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Summary:The mixed volume and the measure of asymmetry for convex bodies are two important topics in convex geometry.In this paper,we first reveal a close connection between the Lp-mixed volumes proposed by E.Lutwak and the p-measures of asymmetry,which have the Minkowski measure as a special case,introduced by Q.Guo.Then,a family of measures of asymmetry is defined in terms of the Orlicz mixed volumes introduced by R.J.Gardner,D.Hug and W.Weil recently,which is an extension of the p-measures.
Bibliography:11-2039/O1
The mixed volume and the measure of asymmetry for convex bodies are two important topics in convex geometry.In this paper,we first reveal a close connection between the Lp-mixed volumes proposed by E.Lutwak and the p-measures of asymmetry,which have the Minkowski measure as a special case,introduced by Q.Guo.Then,a family of measures of asymmetry is defined in terms of the Orlicz mixed volumes introduced by R.J.Gardner,D.Hug and W.Weil recently,which is an extension of the p-measures.
Minkowski measure of asymmetry; p-measure of asymmetry; Lp-mixed volume; Orlicz measure of asymmetry; Orlicz mixed volume
ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 23
ISSN:1439-8516
1439-7617
DOI:10.1007/s10114-014-3502-z