论文标题
Cheeger常数的Blaschke-Lebesgue定理
A Blaschke-Lebesgue Theorem for the Cheeger constant
论文作者
论文摘要
在本文中，我们证明了Reuleaux三角形的一种新的极端特性：它最大化了（相同）常数宽度的所有体之间的脸颊常数。证明依赖于对最佳Reuleaux多边形满足最佳条件的精细分析，以及针对最佳域的Inradius的明确上限。作为一个可能的观点，我们猜想Reuleaux三角形的最大属性具有$ p $ -laplacian的第一个特征值，用于任何$ p \ in（1，+\ infty）$（当前的纸张封面$ p = 1 $，而case $ p = 1 $，而case $ p =+p =+\ f =+\ infty $已知）。
In this paper we prove a new extremal property of the Reuleaux triangle: it maximizes the Cheeger constant among all bodies of (same) constant width. The proof relies on a fine analysis of the optimality conditions satisfied by an optimal Reuleaux polygon together with an explicit upper bound for the inradius of the optimal domain. As a possible perspective, we conjecture that this maximal property of the Reuleaux triangle holds for the first eigenvalue of the $p$-Laplacian for any $p\in (1,+\infty)$ (the current paper covers the case $p=1$ whereas the case $p=+\infty$ was already known).
