The minimal Orlicz surface area

Petty proved that a convex body in Rn has the minimal surface area amongst its SL(n) images, if, and only if, its surface area measure is isotropic. By introducing a new notion of minimal Orlicz surface area, we generalize this result to the Orlicz setting. The analog of Ball's reverse isoperim...

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Bibliographic Details
Published inAdvances in applied mathematics Vol. 61; pp. 25 - 45
Main Authors Zou, Du, Xiong, Ge
Format Journal Article
LanguageEnglish
Published Elsevier Inc 01.10.2014
Subjects
Minimal surface area
Orlicz Brunn–Minkowski theory
Reverse isoperimetric inequality
52A40
Reverse isoperimetric inequality
Minimal surface area
Orlicz Brunn–Minkowski theory
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Summary:Petty proved that a convex body in Rn has the minimal surface area amongst its SL(n) images, if, and only if, its surface area measure is isotropic. By introducing a new notion of minimal Orlicz surface area, we generalize this result to the Orlicz setting. The analog of Ball's reverse isoperimetric inequality is established.
ISSN:0196-8858
1090-2074
DOI:10.1016/j.aam.2014.08.006