The log-Minkowski measure of asymmetry for convex bodies

In this paper, we introduce a new measure of asymmetry, called log-Minkowski measure of asymmetry for planar convex bodies in terms of the L 0 -mixed volume, and show that triangles are the most asymmetric planar convex bodies in the sense of this measure of asymmetry.

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Bibliographic Details
Published inGeometriae dedicata Vol. 196; no. 1; pp. 27 - 34
Main Author Jin, HaiLin
Format Journal Article
LanguageEnglish
Published Dordrecht Springer Netherlands 01.10.2018
Springer Nature B.V
Subjects
Algebraic Geometry
Asymmetry
Convex and Discrete Geometry
Differential Geometry
Hyperbolic Geometry
Mathematics
Mathematics and Statistics
Original Paper
Projective Geometry
Topology
Triangles
Measure of asymmetry
52A10
52A38
Minkowski inequality
Brunn–Minkowski inequality
Mixed volume
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Summary:In this paper, we introduce a new measure of asymmetry, called log-Minkowski measure of asymmetry for planar convex bodies in terms of the L 0 -mixed volume, and show that triangles are the most asymmetric planar convex bodies in the sense of this measure of asymmetry.
ISSN:0046-5755
1572-9168
DOI:10.1007/s10711-017-0302-5