论文标题
RCD空间的几乎最大体积熵的定量刚度和整体RICCI曲率结合
Quantitative rigidity of almost maximal volume entropy for both RCD spaces and integral Ricci curvature bound
论文作者
论文摘要
已知紧凑型度量量度空间的体积熵是该测量的指数增长率，该量度提升到无限范围的通用覆盖率。对于紧凑的Riemannian $ n $ n $ manifold，较低的RICCI曲率结合和上直径绑定，众所周知，只有当它是差异且Gromov-Hausdorff靠近多重苯甲酸空间形式的情况下，它就会承认几乎最大的体积熵。我们证明了$ \ operatotorname {rcd} $的几乎最大体积熵的定量刚度 - 较低的RICCI曲率结合和带有负$ l^p $ integral ricci ricci ricci ricci曲率的riemannian歧管的空格。
The volume entropy of a compact metric measure space is known to be the exponential growth rate of the measure lifted to its universal cover at infinity. For a compact Riemannian $n$-manifold with a negative lower Ricci curvature bound and a upper diameter bound, it was known that it admits an almost maximal volume entropy if and only if it is diffeomorphic and Gromov-Hausdorff close to a hyperbolic space form. We prove the quantitative rigidity of almost maximal volume entropy for $\operatorname{RCD}$-spaces with a negative lower Ricci curvature bound and Riemannian manifolds with a negative $L^p$-integral Ricci curvature lower bound.
