A Maximum Principle for Combinatorial Yamabe Flow

David Glickenstein

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arXiv · math/0211195

A Maximum Principle for Combinatorial Yamabe Flow

David Glickenstein

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Abstract

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.

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BibTeX RIS

David Glickenstein. 2005-06-10. A Maximum Principle for Combinatorial Yamabe Flow. https://arxiv.org/abs/math/0211195

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