关于非正曲率映射的平坦子映射
On flat submaps of maps of non-positive curvature
摘要：
证明了对每个$r>0$，如果非正曲的$(p,q)$ -映射$M$不包含半径为$r$的平坦子映射，则对于某个常数$C$，$M$的面积不超过$Crn$.这加强了Ivanov和Schupp的一个定理。我们证明了一个无限的$(p,q)$ -映射是拟等距于欧氏平面的当且仅当该映射只包含1000个非平坦的顶点和面。我们还推广了Ivanov和Schupp的结果到更大的一类映射，即映射的角度功能。
英文摘要：
We prove that for every $r>0$ if a non-positively curved $(p,q)$-map $M$ contains no flat submaps of radius $r$, then the area of $M$ does not exceed $Crn$ for some constant $C$. This strengthens a theorem of Ivanov and Schupp. We show that an infinite $(p,q)$-map which tessellates the plane is quasi-isometric to the Euclidean plane if and only if the map contains only finitely many non-flat vertices and faces. We also generalize Ivanov and Schupp's result to a much larger class of maps, namely to maps with angle functions.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
