The Orlicz Isoperimetric Inequality

Chang Jian ZHAO

Acta Mathematica Sinica, Chinese Series ›› 2022, Vol. 65 ›› Issue (3) : 513-522.

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Acta Mathematica Sinica, Chinese Series ›› 2022, Vol. 65 ›› Issue (3) : 513-522. DOI: 10.12386/A2022sxxb0042

The Orlicz Isoperimetric Inequality

  • Chang Jian ZHAO
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Abstract

We establish some generalized Orlicz isoperimetric inequalities of convex bodies by using the classical Popoviciu's inequality and Orlicz--Minkowski inequality. The new Orlicz isoperimetric inequality in special case yields the classical isoperimetric inequality, Lp-isoperimetric inequality and Orlicz isoperimetric inequality, respectively.

Key words

convex body / mixed volume / Lp-mixed volume / Popoviciu's inequality

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Chang Jian ZHAO. The Orlicz Isoperimetric Inequality. Acta Mathematica Sinica, Chinese Series, 2022, 65(3): 513-522 https://doi.org/10.12386/A2022sxxb0042

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