组合模与图的类型
Combinatorial modulus and type of graphs
摘要：
设$A$是一个三角化拓扑环的1-骨架。我们建立的组合模上的界限的细化$A'$，形成附加新的顶点和边$A$，只依赖于细化，而不是结构上的$A$本身。这立即适用于表明，一个磁盘三角图可以细化，而不改变其组合类型，提供的细化是不是太疯狂。我们还探讨了磁盘增长的类型问题，证明了一个抛物线条件的基础上的超线性增长率，我们也证明了最佳的。我们证明了我们的结果，没有程度的限制，在EEL和VEL设置和检查类型的问题，更一般的复杂和对偶图。
英文摘要：
Let a $A$ be the 1-skeleton of a triangulated topological annulus. We establish bounds on the combinatorial modulus of a refinement $A'$, formed by attaching new vertices and edges to $A$, that depend only on the refinement and not on the structure of $A$ itself. This immediately applies to showing that a disk triangulation graph may be refined without changing its combinatorial type, provided the refinement is not too wild. We also explore the type problem in terms of disk growth, proving a parabolicity condition based on a superlinear growth rate, which we also prove optimal. We prove our results with no degree restrictions in both the EEL and VEL settings and examine type problems for more general complexes and dual graphs.
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。
