论文标题
固定共轭类在负曲率上的增长
The growth of a fixed conjugacy class in negative curvature
论文作者
论文摘要
令$ m $为可变负曲率的紧凑型封闭歧管。修复基本组$γ$ $ m $的元素$ \ operatorname {id} \ neqγ$，并表示$γ$中的一组元素，这些元素与$γ$ by $ \ operataTornAme {conj}_γ$相连为$γ$。对于$ m $的通用封面中的两个点$ x，y $，我们获得了$ \ operatotorname {conj}_γ$的数量的渐近，$ y $的orbits of $ y $，以$ x $的radius $ t $中心，$ x $，因为$ t $ to $ t $ to to in Infination to Infinity。如果$ m $是二维的，或尺寸$ n \ geq 3 $，并且曲率在上面的$ -1 $及以下为$ - （\ frac {n-1} {n-2} {n-2}）^2 $，我们找到了此计数的指数小错误术语。
Let $M$ be a compact closed manifold of variable negative curvature. Fix an element $\operatorname{id} \neq γ$ in the fundamental group $Γ$ of $M$, and denote the set of elements in $Γ$ that are conjugate to $γ$ by $\operatorname{Conj}_γ$. For two points $x, y$ in the universal cover of $M$, we obtain asymptotics for the number of $\operatorname{Conj}_γ$--orbits of $y$ that lie in a ball of radius $T$ centered at $x$, as $T$ tends to infinity. If $M$ is two-dimensional, or of dimension $n \geq 3$ and curvature bounded above by $-1$ and below by $-(\frac{n-1}{n-2})^2$, we find an exponentially small error term for this count.
