Frontiers of Mathematics in China >
Discrete α-Yamabe flow in 3-dimension
Received date: 10 Jul 2016
Accepted date: 18 Sep 2016
Published date: 06 Jul 2017
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We generalize the discrete Yamabe flow to αorder. This Yamabe flow deforms the α-order curvature to a constant. Using this new flow, we manage to find discrete α-quasi-Einstein metrics on the triangulations of .
Key words: α-Yamabe flow; α-quasi Einstein metric; ball packing metric
Huabin GE , Shiguang MA . Discrete α-Yamabe flow in 3-dimension[J]. Frontiers of Mathematics in China, 2017 , 12(4) : 843 -858 . DOI: 10.1007/s11464-016-0603-2
1 |
CooperD, RivinI. Combinatorial scalar curvature and rigidity of ball packings. Math Res Lett, 1996, 3: 51–60
|
2 |
GeH, JiangW. On the deformation of discrete conformal factors on surfaces. Calc Var Partial Differential Equations (to appear)
|
3 |
GeH, XuX. Discrete quasi-Einstein metrics and combinatorial curvature flows in 3-dimension. Adv Math, 2014, 267: 470–497
|
4 |
GeH, XuX. A combinatorial Yamabe problem on two and three dimensional manifolds. arXiv: 1504.05814 [math.DG]
|
5 |
GeH, XuX. 2-dimensional combinatorial Calabi flow in hyperbolic background geometry. Differential Geom Appl, 2016, 47: 86–98
|
6 |
GeH, XuX. A discrete Ricci flow on surfaces with hyperbolic background geometry. Int Math Res Not IMRN,
|
7 |
GeH, XuX. α-curvatures and α-flows on low dimensional triangulated manifolds. Calc Var Partial Differential Equations, 2016, 55(1): Art 12 (16 pp)
|
8 |
GlickensteinD. A combinatorial Yamabe flow in three dimensions. Topology, 2005, 44(4): 791–808
|
9 |
GlickensteinD. A maximum principle for combinatorial Yamabe flow. Topology, 2005, 44(4): 809–825
|
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