The log-Minkowski measure of asymmetry for convex bodies

Original Paper


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.


Measure of asymmetry Mixed volume Brunn–Minkowski inequality Minkowski inequality 

Mathematics Subject Classification

52A10 52A38 



The author is grateful to the referees for their valuable suggestions and comments.


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© Springer Science+Business Media B.V., part of Springer Nature 2017

Authors and Affiliations

  1. 1.Department of MathematicsSuzhou University of Science and TechnologySuzhouChina

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