[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.4134/BKMS.b160583

UNIFIED (α, β)-FLOWS ON TRIANGULATED MANIFOLDS WITH TWO AND THREE DIMENSIONS

Ge, Huabin (Department of Mathematics Beijing Jiaotong University)
Li, Ming (LSEC, ICMSEC Academy of Mathematics and Systems Science Chinese Academy of Sciences)

Publication Information

Bulletin of the Korean Mathematical Society / v.54, no.4, 2017 , pp. 1361-1371 More about this Journal

Abstract

In this paper, we introduce a framework of ( ${\alpha},{\beta}$ )-flows on triangulated manifolds with two and three dimensions, which unifies several discrete curvature flows previously defined in the literature.

Keywords

circle packing metric; discrete Ricci flow; ( ${\alpha},{\beta}$ )-flows; triangulation;

Citations & Related Records

Reference

1	B. Chow and F. Luo, Combinatorial Ricci flows on surfaces, J. Differential Geom. 63 (2003), no. 1, 97-129. DOI
2	D. Cooper and I. Rivin, Combinatorial scalar curvature and rigidity of ball packings, Math. Res. Lett. 3 (1996), no. 1, 51-60. DOI
3	H. Ge, Combinatorial Calabi flows on surfaces, Trans. Amer. Math. Soc., online, DOI: https://doi.org/10.1090/tran/7196. DOI
4	H. Ge and W. Jiang, A combinatorial Yamabe flow with normalization, Preprint.
5	H. Ge and S. Ma, Discrete ${\alpha}$ -Yamabe flow in 3-dimension, Front. Math. China 12 (2017), no. 4, 843-858. DOI
6	H. Ge and S. Ma, On the ${\alpha}$ -modified combinatorial Yamabe flow in three dimension, Preprint.
7	H. Ge and X. Xu, Discrete quasi-Einstein metrics and combinatorial curvature flows in 3-dimension, Adv. Math. 267 (2014), 470-497. DOI
8	H. Ge and X. Xu, A combinatorial Yamabe problem on two and three dimensional manifolds, arXiv:1504.05814 [math.DG].
9	H. Ge and X. Xu, ${\alpha}$ -curvatures and ${\alpha}$ -flows on low dimensional triangulated manifolds, Calc. Var. Partial Differential Equations 55 (2016), no. 1, Art. 12, 16 pp.
10	D. Glickenstein, A combinatorial Yamabe flow in three dimensions, Topology 44 (2005), no. 4, 791-808. DOI
11	D. Glickenstein, A maximum principle for combinatorial Yamabe flow, Topology 44 (2005), no. 4, 809-825. DOI
12	R. S. Hamilton, Three-manifolds with positive Ricci curvature, J. Differential Geom. 17 (1982), no. 2, 255-306. DOI
13	F. Luo, Combinatorial Yamabe flow on surfaces, Commun. Contemp. Math. 6 (2004), no. 5, 765-780. DOI
14	I. Rivin, An extended correction to "Combinatorial Scalar Curvature and Rigidity of Ball Packings," (by D. Cooper and I. Rivin), arXiv:math/0302069v2 [math.MG].
15	W. Thurston, Geometry and Topology of 3-manifolds, Princeton lecture notes 1976.