A Maximum Principle for Combinatorial Yamabe Flow
摘要
This article studies a discrete geometric structure on triangulated manifolds and an associated curvature flow (combinatorial Yamabe flow). The associated evolution of curvature appears to be like a heat equation on graphs, but it can be shown to not satisfy the maximum principle. The notion of a parabolic-like operator is introduced as an operator which satisfies the maximum principle, but may not be parabolic in the usual sense of operators on graphs. A maximum principle is derived for the curvature of combinatorial Yamabe flow under certain assumptions on the triangulation, and hence the heat operator is shown to be parabolic-like. The maximum principle then allows a characterization of the curvature as well was a proof of long term existence of the flow.
引用
@article{arxiv.math/0211195,
title = {A Maximum Principle for Combinatorial Yamabe Flow},
author = {David Glickenstein},
journal= {arXiv preprint arXiv:math/0211195},
year = {2007}
}
备注
20 pages, this is an almost entirely different paper. Some elements of the old version are in the paper arxiv:math.MG/0506182