JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2024, Vol. 59 ›› Issue (8): 113-117, 126.doi: 10.6040/j.issn.1671-9352.0.2023.033

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Integral inequality of Wulff curvature for plane convex bodies

Yaling WANG(),Xu DONG,Chunna ZENG*()   

  1. School of Mathematical Sciences, Chongqing Normal University, Chongqing 401331, China
  • Received:2023-01-12 Online:2024-08-20 Published:2024-07-31
  • Contact: Chunna ZENG E-mail:wangyl7228@163.com;zengchn@163.com

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Abstract:

In this paper, we mainly study the integral inequality of Wulff curvature in the case of Wulff flow on the plane. By using Green-Osher inequality and Wulff-Steiner polynomials, we obtain the Wulff curvature integral inequality of any power of symmetric and nonsymmetric convex bodies. Specifically, when one of the convex bodies is an unit circle, the curvature integral inequality of any powers of the plane convex curve is obtained.

Key words: convex body, Steiner polynomial, Green-Osher inequality, Wulff curvature, Wulff-Steiner polynomial

CLC Number: 

  • O186.5
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