https://neckpinch.com/authors/xiang-zhu/New arXiv papers by Xiang Zhu, from Neckpinch Tue, 03 Nov 2026 08:41:12 GMT https://neckpinch.com/papers/2311.04450/arxiv:2311.04450Wed, 08 Nov 2023 00:00:00 GMTXiang Zhu — In this paper, we prove that given a hyperbolic polyhedral metric with an inversive distance circle packing, and a target discrete curvature satisfying Gauss-Bonnet formula, there exist a unique inversive distance circle packing which is discrete conformal to the former one. We deform the surface by discrete Ricci flow, and do surgery by edge flipping when the orthogonal circles of some faces are about to be non-compact. The revised weighted Delaunay inequality of hyperbolic case implies the compactness of the orthogonal circle. We use a variational principle of a convex Ricci potential defined on the fiber bundles with cell-decomposition and differential structure based on Teichmüller space to finish the proof.Ricci flowSurgeryLimit spaces & RCDBoundaries & non-compactDiscrete & graph Ricci https://neckpinch.com/papers/2311.01272/arxiv:2311.01272Thu, 02 Nov 2023 00:00:00 GMTXiang Zhu — We prove that for any discrete curvature satisfying Gauss-Bonnet formula, there exist a unique up to scaling inversive distance circle packing in the discrete conformal equivalent class, whose polyhedral metric meets the target curvature. We prove it by constructing diffeomorphism between fiber bundles with cell decomposition based on Teichmüller spaces, and each discrete conformal equivalent class is a fiber passing through finite cell with respect to triangulations, which means we can do surgery on the discrete Ricci flow by edge flipping using a generalized Ptolemy equation to ensure it converge and never blow up.Ricci flowSingularitiesSurgeryDiscrete & graph Ricci