关于平面上具有重心距离的定量等周不等式
On the quantitative isoperimetric inequality in the plane with the barycentric distance
摘要：
本文研究了平面上的以下定量等周不等式：$λ_0^2(Ω) \leq C δ(Ω)$其中$δ$是等周亏额，$λ_0$是重心不对称性.我们的目的是推广B. Fuglede在\cite{Fu93Geometriae}中。为此目的，我们考虑形状最优化问题：最小化的比例$δ(Ω)/λ_0^2(Ω)$在类的紧连接集和类的凸集。
英文摘要：
In this paper we study the following quantitative isoperimetric inequality in the plane: $λ_0^2(Ω) \leq C δ(Ω)$ where $δ$ is the isoperimetric deficit and $λ_0$ is the barycentric asymmetry. Our aim is to generalize some results obtained by B. Fuglede in \cite{Fu93Geometriae}. For that purpose, we consider the shape optimization problem: minimize the ratio $δ(Ω)/λ_0^2(Ω)$ in the class of compact connected sets and in the class of convex sets.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
