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Forum Mathematicum

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Volume 30, Issue 4

Issues

Orlicz dual affine quermassintegrals

Chang-Jian Zhao
Published Online: 2017-12-13 | DOI: https://doi.org/10.1515/forum-2017-0174

Abstract

In the paper, our main aim is to generalize the dual affine quermassintegrals to the Orlicz space. Under the framework of Orlicz dual Brunn–Minkowski theory, we introduce a new affine geometric quantity by calculating the first-order variation of the dual affine quermassintegrals, and call it the Orlicz dual affine quermassintegral. The fundamental notions and conclusions of the dual affine quermassintegrals and the Minkoswki and Brunn–Minkowski inequalities for them are extended to an Orlicz setting, and the related concepts and inequalities of Orlicz dual mixed volumes are also included in our conclusions. The new Orlicz–Minkowski and Orlicz–Brunn–Minkowski inequalities in a special case yield the Orlicz dual Minkowski inequality and Orlicz dual Brunn–Minkowski inequality, which also imply the Lp-dual Minkowski inequality and Brunn–Minkowski inequality for the dual affine quermassintegrals.

Keywords: Star body; Orlicz harmonic radial addition; affine quermassintegral; dual affine quermassintegral; Orlicz–Minkowski inequality; Orlicz–Brunn–Minkowski inequality

MSC 2010: 52A30; 52A40; 46E30

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About the article


Received: 2017-08-14

Revised: 2017-10-27

Published Online: 2017-12-13

Published in Print: 2018-07-01


Funding Source: National Natural Science Foundation of China

Award identifier / Grant number: 11371334

Research is supported by National Natural Science Foundation of China (11371334).


Citation Information: Forum Mathematicum, Volume 30, Issue 4, Pages 929–945, ISSN (Online) 1435-5337, ISSN (Print) 0933-7741, DOI: https://doi.org/10.1515/forum-2017-0174.

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