Conference abstracts

Session A4 - Computational Geometry and Topology

July 10, 16:00 ~ 16:25

Local Geometric Convergence of Embedded Graphs

Benjamin Schweinhart

Ohio State Unversity, United States   -

We introduce a notion of local geometric convergence for embedded graphs in $\mathbb{R}^n$, developed in analogy with Benjamini-Schramm convergence of abstract graphs. It is defined in terms of weak convergence of probability measures on the space of embedded graphs with a smooth topology. We provide hypotheses under which it is implied by convergence of the first Wasserstein metric induced by the local Hausdorff distance. These concepts are used to state a universality conjecture for the long-term behavior of graphs evolving by curvature flow, and to test it computationally.

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