论文标题
在非碰撞情况下，几乎最大的体积熵刚度
Almost maximal volume entropy rigidity for integral Ricci curvature in the non-collapsing case
论文作者
论文摘要
在本说明中，我们将显示在非碰撞情况下绑定的较低积分ricci曲率的歧管几乎最大的熵刚度：给定$ n，d，p> \ frac {n} {2} $，存在$Δ（n，d，d，d，d，d，d，d，d，d，d，d，d，d，d，d，d，d，d，d，d，d，p） d，p）$，如果一个紧凑的$ n $ -n $ manifold $ m $满足整体curvature ricci曲率的下限$ \ bar k（-1，p）\leqΔ$，diameter $ diamoter $ diam（m）\ leq d $ and voluge enturepropy $ h（m）\ geq n-1-- $ $ m $ m $ m $ m $ m $ m $ m $ m $ m $ m $ m $ m $ m $ m $ m $ $ \ bbb h^k $，$ k \ leq n $;如果此外，如果$ m $，$ vol（m）\ geq v> 0 $，则$ m $是diffeomorphic的，而gromov-hausdorff靠近双曲线歧管，其中$δ，ε$也取决于$ v $。
In this note we will show the almost maximal volume entropy rigidity for manifolds with lower integral Ricci curvature bound in the non-collapsing case: Given $n, d, p>\frac{n}{2}$, there exist $δ(n, d, p), ε(n, d, p)>0$, such that for $δ<δ(n, d, p)$, $ε<ε(n, d, p)$, if a compact $n$-manifold $M$ satisfies that the integral Ricci curvature has lower bound $\bar k(-1, p)\leq δ$, the diameter $diam(M)\leq d$ and volume entropy $h(M)\geq n-1-ε$, then the universal cover of $M$ is Gromov-Hausdorff close to a hyperbolic space form $\Bbb H^k$, $k\leq n$; If in addition the volume of $M$, $vol(M)\geq v>0$, then $M$ is diffeomorphic and Gromov-Hausdorff close to a hyperbolic manifold where $δ, ε$ also depends on $v$.
