论文标题
亚历山德罗夫空间上的定量最大体积熵刚度
Quantitative maximal volume entropy rigidity on Alexandrov spaces
论文作者
论文摘要
我们将表明，定量最大体积熵刚度在Alexandrov空间上。更准确地说，给定$ n，d $，存在$ε（n，d）> 0 $，以至于对于$ε<ε（n，d）$，如果$ x $是$ n $ dimensional-dimensional alexandrov space，curvature $ \ geq-geq -1 $，$ \ geq -1 $，$ \ perperatornArname {diamname {diam}（diam}（x） Gromov-Hausdorff接近双曲线歧管。该结果将\ cite {Crx}的定量最大体积熵刚度扩展到Alexandrov空间。我们还将为$ \ op {rcd}^*$ - 在非碰撞情况下的$ \ op {rcd}^*$ - 空格提供定量的最大音量熵刚度。
We will show that the quantitative maximal volume entropy rigidity holds on Alexandrov spaces. More precisely, given $N, D$, there exists $ε(N, D)>0$, such that for $ε<ε(N, D)$, if $X$ is an $N$-dimensional Alexandrov space with curvature $\geq -1$, $\operatorname{diam}(X)\leq D, h(X)\geq N-1-ε$, then $X$ is Gromov-Hausdorff close to a hyperbolic manifold. This result extends the quantitive maximal volume entropy rigidity of \cite{CRX} to Alexandrov spaces. And we will also give a quantitative maximal volume entropy rigidity for $\op{RCD}^*$-spaces in the non-collapsing case.
