https://neckpinch.com/authors/tianqi-wu/New arXiv papers by Tianqi Wu, from Neckpinch Tue, 03 Nov 2026 07:15:30 GMT https://arxiv.org/abs/2312.01698arxiv:2312.01698Mon, 04 Dec 2023 00:00:00 GMTTianqi Wu — We prove that for a convex polytope decomposition of a domain in ℝⁿ, 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.Yamabe flow https://arxiv.org/abs/2107.14102arxiv:2107.14102Thu, 29 Jul 2021 00:00:00 GMTTianqi Wu, Xu Xu — Using the fractional discrete Laplace operator for triangle meshes, we introduce a fractional combinatorial Calabi flow for discrete conformal structures on surfaces, which unifies and generalizes Chow-Luo's combinatorial Ricci flow for Thurston's circle packings, Luo's combinatorial Yamabe flow for vertex scaling and the combinatorial Calabi flow for discrete conformal structures on surfaces. For Thurston's Euclidean and hyperbolic circle packings on triangulated surfaces, we prove the longtime existence and global convergence of the fractional combinatorial Calabi flow. For vertex scalings on polyhedral surfaces, we do surgery on the fractional combinatorial Calabi flow by edge flipping under the Delaunay condition to handle the potential singularities along the flow. Using the discrete conformal theory established by Gu et al., we prove the longtime existence and global convergence of the fractional combinatorial Calabi flow with surgery.Ricci flowYamabe flowOther curvature flowsSingularitiesSurgeryGeometrizationSurfacesKähler geometryLong-time existence & convergenceDiscrete & graph Ricci