Paper · Sep 28, 2017

Unified -Flows on Triangulated Manifolds with Two and Three Dimensions

Huabin Ge, Ming Li

math.GTWider flowsarXiv:1709.09877
View PDF View HTML arXiv page

As on arXiv

Abstract

In this paper, we introduce a framework of -flows on triangulated manifolds with two and three dimensions, which unifies several discrete curvature flows previously defined in the literature.

View PDF View HTML arXiv page
Submitted
Sep 28, 2017
Subjects
math.GT, math.AP, math.DG
Journal
Bull. Korean Math. Soc., 54 (2017), no. 4, 1361-1371
DOI
10.4134/BKMS.b160583

Comments: 12 pages, all comments are welcome

Other curvature flowsDiscrete & graph Ricci

Its neighbourhood

Connected papers

The 8 papers on this site closest to this one, judged by the topics they share, the words and phrases in their titles and abstracts, and their authors. They are not its citations, but a map of the work around it. Papers here go back to 2016, plus the canon.

Connected papers This paper in the centre and the 8 papers closest to it around it, in date order clockwise from the top. The closer a paper sits to the centre, the stronger the connection. This paper On the deformation of discrete conformal factors on surfaces (Huabin Ge and Wenshuai Jiang, 2016)7Ge 2016 On a combinatorial curvature for surfaces with inversive distance circle packing metrics (Huabin Ge and Xu Xu, 2017)1Ge 2017 Combinatorial Ricci flows and the hyperbolization of a class of compact 3-manifolds (Ke Feng, Huabin Ge and Bobo Hua, 2020)5Feng 2020 Combinatorial Ricci flows with applications to the hyperbolization of cusped 3-manifolds (Ke Feng, Huabin Ge and Bobo Hua, 2020)8Feng 2020 A combinatorial curvature flow in spherical background geometry (Huabin Ge, Bobo Hua and Puchun Zhou, 2023)2Ge 2023 Combinatorial Ricci flows on infinite disk triangulations (Huabin Ge, Bobo Hua and Puchun Zhou, 2025)6Ge 2025 Characterization of Infinite Ideal Polyhedra in Hyperbolic 3-Space via Combinatorial Ricci Flow (Huabin Ge, Bobo Hua, Hao Yu et al., 2025)4Ge 2025 Combinatorial Calabi flows on infinitely triangulated surfaces (Yuerong Bian and Xu Xu, 2026)3Bian 2026
Closer to the centre: more closely connected. Clockwise from the top: oldest to newest. Ricci flowWider flowsalso connected to each other
  1. On a combinatorial curvature for surfaces with inversive distance circle packing metrics

    Huabin Ge and Xu Xu

    Topics Discrete & graph Ricci · Same author Huabin Ge · Shared terms “triangulated”

  2. A combinatorial curvature flow in spherical background geometry

    Huabin Ge, Bobo Hua and Puchun Zhou

    Topics Discrete & graph Ricci, Other curvature flows · Same author Huabin Ge

  3. Combinatorial Calabi flows on infinitely triangulated surfaces

    Yuerong Bian and Xu XuWider flows

    Topics Discrete & graph Ricci, Other curvature flows · Shared terms “triangulated”

  4. Characterization of Infinite Ideal Polyhedra in Hyperbolic 3-Space via Combinatorial Ricci Flow

    Huabin Ge, Bobo Hua, Hao Yu et al.

    Topics Discrete & graph Ricci · Same author Huabin Ge

  5. Combinatorial Ricci flows and the hyperbolization of a class of compact 3-manifolds

    Ke Feng, Huabin Ge and Bobo Hua

    Topics Discrete & graph Ricci · Same author Huabin Ge

  6. Combinatorial Ricci flows on infinite disk triangulations

    Huabin Ge, Bobo Hua and Puchun Zhou

    Topics Discrete & graph Ricci · Same author Huabin Ge

  7. On the deformation of discrete conformal factors on surfaces

    Huabin Ge and Wenshuai JiangWider flows

    Topics Discrete & graph Ricci · Same author Huabin Ge

  8. Combinatorial Ricci flows with applications to the hyperbolization of cusped 3-manifolds

    Ke Feng, Huabin Ge and Bobo Hua

    Topics Discrete & graph Ricci · Same author Huabin Ge

Read around it

Background reading

The guides for the topics of this paper: what each idea is, why it matters, and the papers to read first.

Other curvature flows Wider flows Flows that move a hypersurface or metric by some other function of curvature: Gauss curvature (worn stones), inverse mean curvature (the Penrose… Start with: Shapes of worn stones (Firey, 1974) Discrete & graph Ricci Curvature and Ricci flow for graphs, networks and triangulated surfaces. It runs from Chow–Luo's combinatorial flow on circle packings to Ollivier's… Start with: Combinatorial Ricci Flows on Surfaces (Chow et al., 2002)

In the guidebook

  1. 6D.11
    Computing Geometric FlowsBook 6D · Diffusions, Finance and Computation

    Numerical curve shortening and mean curvature flow, level sets and phase fields, discrete Ricci flow on surfaces and in conformal mapping, rotationally symmetric neckpinches, and what computation has taught about singularities.