https://neckpinch.com/authors/shiping-liu/New arXiv papers by Shiping Liu, from Neckpinch Tue, 03 Nov 2026 07:15:30 GMT https://arxiv.org/abs/2608.05939arxiv:2608.05939Thu, 06 Aug 2026 00:00:00 GMTShiping Liu, Yunyan Yang — In this note, we prove that, on weighted graphs, the Lin–Lu–Yau curvature coincides with the p-Ollivier curvature up to scaling whenever the idleness parameter p≥ 1/2. Moreover, the threshold 1/2 is sharp. This extends an earlier result of Bourne et al. (Ollivier–Ricci idleness functions of graphs, SIAM J. Discrete Math., 32 (2018), no. 2, 1408-1424), where combinatorial graphs were considered. This observation yields a simple proof for the global existence and uniqueness of solutions of the Lin–Lu–Yau curvature flow in Bai et al. (Ollivier Ricci-flow on weighted graphs, Amer. J. Math. 146 (2024), 1723-1747).Ricci flowOther curvature flowsStability & uniquenessLong-time existence & convergenceDiscrete & graph Ricci https://arxiv.org/abs/2212.12401arxiv:2212.12401Fri, 23 Dec 2022 00:00:00 GMTDavid Cushing, Supanat Kamtue, Shiping Liu, Florentin Münch, Norbert Peyerimhoff, Ben Snodgrass — In this second part of a sequence of two papers, we discuss the implementation of a curvature flow on weighted graphs based on the Bakry-Émery calculus. This flow can be adapted to preserve the Markovian property and its limits as time goes to infinity turn out to be curvature sharp weighted graphs. After reviewing some of the main results of the first paper concerned with the theoretical aspects, we present various examples (random graphs, paths, cycles, complete graphs, wedge sums and Cartesian products of complete graphs, hypercubes) and exhibit further properties of this flow. One particular aspect in our investigations is asymptotic stability and instability of curvature flow equilibria. The paper ends with a description of the available Python functions and routines available in the ancillary file. We hope that the explanations of the Python implementation via examples will help users to carry out their own curvature flow experiments.Other curvature flowsLimit spaces & RCDStability & uniqueness https://arxiv.org/abs/2204.10064arxiv:2204.10064Thu, 21 Apr 2022 00:00:00 GMTDavid Cushing, Supanat Kamtue, Shiping Liu, Florentin Münch, Norbert Peyerimhoff, Hugo Benedict Snodgrass — In this sequence of two papers, we introduce a curvature flow on (mixed) weighted graphs which is based on the Bakry-Émery calculus. The flow is described via a time-continuous evolution through the weighting schemes. By adapting this flow to preserve the Markovian property, its limits turn out to be curvature sharp. Our aim is to present the flow in the most general case of not necessarily reversible random walks allowing laziness, including vanishing transition probabilities along some edges ("degenerate" edges). This approach requires to extend all concepts (in particular, the Bakry-Émery curvature related notions) to this general case and it leads to a distinction between the underlying topology (a mixed combinatorial graph) and the weighting scheme (given by transition rates). We present various results about curvature sharp vertices and weighted graphs as well as some fundamental properties of this new curvature flow. This paper is accompanied by a second paper discussing the curvature flow implementation in Python for practical use. In this second paper we present examples and exhibit further properties of the flow.Other curvature flowsLimit spaces & RCD