The Minimal Perimeter of a Log-Concave Function

Niufa Fang and Zengle Zhang
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Niufa Fang: Chern Institute of Mathematics, Nankai University, Tianjin 300071, China
Zengle Zhang: Key Laboratory of Group and Graph Theories and Applications, Chongqing University of Arts and Sciences, Chongqing 402160, China

Mathematics, 2020, vol. 8, issue 8, 1-11

Abstract: Inspired by the equivalence between isoperimetric inequality and Sobolev inequality, we provide a new connection between geometry and analysis. We define the minimal perimeter of a log-concave function and establish a characteristic theorem of this extremal problem for log-concave functions analogous to convex bodies.

Keywords: isoperimetric problem; minimal perimeter; log-concave functions; isotropic measure (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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