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2016 The Minimal Dual Orlicz Surface Area
Tongyi Ma
Taiwanese J. Math. 20(2): 287-309 (2016). DOI: 10.11650/tjm.20.2016.6632


Petty proved that a convex body in $\mathbb{R}^{n}$ has the minimal surface area among its $\operatorname{SL}(n)$ images if and only if its surface area measure is isotropic. Recently, Zou and Xiong generalized this result to the Orlicz setting by introducing a new notion of minimal Orlicz surface area, and the analog of Ball's reverse isoperimetric inequality is established. In this paper, we give the dual results in Orlicz space by introducing a new notion of minimal dual Orlicz surface area. And the dual form of Ball's isoperimetric inequality is established.


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Tongyi Ma. "The Minimal Dual Orlicz Surface Area." Taiwanese J. Math. 20 (2) 287 - 309, 2016.


Published: 2016
First available in Project Euclid: 1 July 2017

zbMATH: 1357.52010
MathSciNet: MR3481386
Digital Object Identifier: 10.11650/tjm.20.2016.6632

Primary: 52A30 , 52A40

Keywords: Convex bodies , Isoperimetric inequality , isotropic measure , minimal dual Orlicz surface area , star bodies

Rights: Copyright © 2016 The Mathematical Society of the Republic of China


Vol.20 • No. 2 • 2016
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