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The Minimal Perimeter of a Log-Concave Function

Author

Listed:
  • 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)

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.

Suggested Citation

  • Niufa Fang & Zengle Zhang, 2020. "The Minimal Perimeter of a Log-Concave Function," Mathematics, MDPI, vol. 8(8), pages 1-11, August.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:8:p:1365-:d:399144
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