Orlicz mixed chord-integrals

In this paper, we introduce an affine geometric quantity and call it Orlicz mixed chord integral by defining a new Orlicz chord addition, which generalizes the mixed chord integrals to Orlicz space. The Minkoswki and Brunn-Minkowski inequalities for the Orlicz mixed chord integrals are established....

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Bibliographic Details
Published inAIMS mathematics Vol. 5; no. 6; pp. 6639 - 6656
Main Author Chang-Jian Zhao
Format Journal Article
LanguageEnglish
Published AIMS Press 01.01.2020
Subjects
chord integral
first order variation
l_{p}$-mixed chord integral
mixed chord integral
orlicz chord addition
orlicz mixed chord integral
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Summary:In this paper, we introduce an affine geometric quantity and call it Orlicz mixed chord integral by defining a new Orlicz chord addition, which generalizes the mixed chord integrals to Orlicz space. The Minkoswki and Brunn-Minkowski inequalities for the Orlicz mixed chord integrals are established. The new inequalities in special cases yield $L_{p}$-Minkowski and Brunn-Minkowski inequalities for the chord integrals. The related concepts and inequalities of $L_{p}$-mixed chord integrals are derived. As an application, a new isoperimetric inequality for the chord integrals is given. As extensions, Orlicz multiple mixed chord integrals and Orlicz-Aleksandrov-Fenchel inequality for the Orlicz multiple mixed chord integrals are also derived here for the first time.
ISSN:2473-6988
DOI:10.3934/math.2020427