论文标题
连续的施泰纳对齐对对称性的应用与blaschke-santaló图
An application of the continuous Steiner symmetrization to Blaschke-Santaló diagrams
论文作者
论文摘要
在本文中，我们考虑了Brock在\ cite {bro95，bro00}中引入的{\ it连续施泰纳对称性}的所谓过程。它将每个域$ω\ subset \ subset \ mathbb {r}^d $转换为球，使体积固定并让第一个特征值和扭转分别减少和增加。虽然通常不能提供$γ$ - 连续的地图$ t \ t \mapstoΩ_t$，但可以稍微修改，因此要获得$γ$浓度的域$ω$的$γ$ - 接收性，也就是说，即$ \ \ mathbb r}^d $。这允许获得对扭转和特征值的蓝奇 - 桑塔尔图的尖锐表征。
In this paper we consider the so-called procedure of {\it Continuous Steiner Symmetrization}, introduced by Brock in \cite{bro95,bro00}. It transforms every domain $Ω\subset\subset\mathbb{R}^d$ into the ball keeping the volume fixed and letting the first eigenvalue and the torsion respectively decrease and increase. While this does not provide, in general, a $γ$-continuous map $t\mapstoΩ_t$, it can be slightly modified so to obtain the $γ$-continuity for a $γ$-dense class of domains $Ω$, namely, the class of polyedral sets in $\mathbb{R}^d$. This allows to obtain a sharp characterization of the Blaschke-Santaló diagram of torsion and eigenvalue.
