A REFINED REVERSE ISOPERIMETRIC INEQUALITY IN THE PLANE

作者：Pan, Shengliang^*; Tang, Xueyuan; Wang, Xiaoyu

来源：Mathematical Inequalities & Applications, 2010, 13(2): 329-338.

DOI：10.7153/mia-13-26

• Minkowski's support function
• locus of centers of curvature
• integral of radius of curvature
• reverse isoperimetric inequality

It is proved that if gamma is a closed strictly convex curve in the plane with length L and area A, then
L(2) <= 4 pi A 2 pi vertical bar(A) over tilde vertical bar,
with equality holding if and only if gamma is a circle, where (A) over tilde vertical bar denotes the oriented area enclosed by the locus of curvature centers of gamma.

• 出版日期2010-4
• 单位华东师范大学; 合肥师范学院