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 metric on the hexagonal lattice.
Flows of piecewise analytic vector fields in convex polytope decompositions
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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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The existence and uniqueness of infinite combinatorial Yamabe flows
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 metric on the hexagonal lattice.