A GENERALIZATION OF THE BLASCHKE-LEBESGUE PROBLEM TO A KIND OF CONVEX DOMAINS

作者:Pan Shengliang*; Zhang Deyan; Chao Zhongjun
来源:Discrete and Continuous Dynamical Systems-Series B, 2016, 21(5): 1587-1601.
DOI:10.3934/dedsb.2016012

摘要

In this paper we will introduce for a convex domain K in the Euclidean plane a function Omega(n)(K, theta) which is called by us the biwidth of K, and then try to find out the least area convex domain with constant biwidth Lambda among all convex domains with the same constant biwidth. When n is an odd integer, it is proved that our problem is just that of Blaschke-Lebesgue, and when n is an even number, we give a lower bound of the area of such constant biwidth domains.

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