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A generalization of the Blaschke-Lebesgue problem to a kind of convex domains

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  • 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.
    Mathematics Subject Classification: Primary: 52A38, 52A15; Secondary: 52A40.


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