论文标题
平均面积比和归一化双曲线n-manifolds的总标数曲率
Average area ratio and normalized total scalar curvature of hyperbolic n-manifolds
论文作者
论文摘要
在封闭的尺寸的封闭双曲歧管上$ n \ geq 3 $，我们回顾了与$ r_h \ geq -n（n -1）$相对于双曲线公制$ h_0 $的平均面积比的定义，我们证明，它在$ H_0 $ $ H_0 $中获得了当地版本的GROMOV的最低限度，该公司的最低最低限度为$ h_0 $。此外，我们讨论了双曲线$ n $ manifolds的平均面积比与标准化的总标态曲率之间的关系，以及如果$ n $奇怪的话，它与最小的表面熵之间的关系。
On closed hyperbolic manifolds of dimension $n\geq 3$, we review the definition of the average area ratio of a metric $h$ with $R_h\geq -n(n-1)$ relative to the hyperbolic metric $h_0$, and we prove that it attains the local minimum of one at $h_0$, which solves a local version of Gromov's conjecture. Additionally, we discuss the relation between the average area ratio and normalized total scalar curvature for hyperbolic $n$-manifolds, as well as its relation to the minimal surface entropy if $n$ is odd.
