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Flows of piecewise analytic vector fields in convex polytope decompositions

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arxiv 2312.01698 v1 pith:4DD3N4WZ submitted 2023-12-04 math.GT math.CA

Tianqi Wu This is my paper · ORCID
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keywords analyticconvexdecompositionpiecewisepolytopeprovevectorchopped
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abstract

We prove that for a convex polytope decomposition of a domain in $\mathbb R^n$, an integral curve of a piecewise analytic vector field is chopped by the decomposition into finitely many pieces. As a consequence, we prove the finiteness of the number of the edge flips in a discrete Yamabe flow.

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  1. The existence and uniqueness of infinite combinatorial Yamabe flows

    math.DG 2025-07 conditional novelty 6.0 of 10

    The infinite combinatorial Yamabe flow exists locally and uniquely on uniformly nondegenerate, uniformly Delaunay triangulations with bounded degree, has a globally defined extension, and converges near the regular me...

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