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Results in Mathematics

, 73:26 | Cite as

An Extremal Property of p-mean Width

  • Qunli Long
  • Songjun Lv
Article

Abstract

Several isoperimetric type inequalities for p-mean width of convex bodies in \(\mathbb {R}^n\) are established. These inequalities show the interrelations among the p-mean width of a convex body in \(\mathbb {R}^n\), an isotropic measure on unit sphere, and the newly-introduced \(L_{r,s}\)-pseudo-moment body of the given body in \(\mathbb {R}^n\). The equalities in these inequalities are all characterized by parallelotopes.

Keywords

Isoperimetric inequality p-mean width isotropic measure optimal transportation generalized \(L_\infty \) parallelotope 

Mathematics Subject Classification

52A40 

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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.School of Mathematical SciencesChongqing Normal UniversityChongqingChina

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