On combinatorial Calabi flow with hyperbolic circle patterns
In this paper, we prove the long time existence of the combinatorial Calabi flow in hyperbolic background geometry and the convergence of the flow to a smooth hyperbolic surface under Thurston's combinatorial condition in full generality, which improves the result in [14]. This flow provides a...
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| Published in | Advances in mathematics (New York. 1965) Vol. 333; pp. 523 - 538 |
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| Main Authors | , |
| Format | Journal Article |
| Language | English |
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31.07.2018
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| ISSN | 0001-8708 1090-2082 |
| DOI | 10.1016/j.aim.2018.05.039 |
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| Abstract | In this paper, we prove the long time existence of the combinatorial Calabi flow in hyperbolic background geometry and the convergence of the flow to a smooth hyperbolic surface under Thurston's combinatorial condition in full generality, which improves the result in [14]. This flow provides a natural algorithm to find Thurston's hyperbolic circle patterns. |
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| AbstractList | In this paper, we prove the long time existence of the combinatorial Calabi flow in hyperbolic background geometry and the convergence of the flow to a smooth hyperbolic surface under Thurston's combinatorial condition in full generality, which improves the result in [14]. This flow provides a natural algorithm to find Thurston's hyperbolic circle patterns. |
| Author | Ge, Huabin Hua, Bobo |
| Author_xml | – sequence: 1 givenname: Huabin surname: Ge fullname: Ge, Huabin email: hbge@bjtu.edu.cn organization: Department of Mathematics, Beijing Jiaotong University, Beijing 100044, PR China – sequence: 2 givenname: Bobo surname: Hua fullname: Hua, Bobo email: bobohua@fudan.edu.cn organization: School of Mathematical Sciences, LMNS, Fudan University, Shanghai 200433, PR China |
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| Cites_doi | 10.1016/j.gmod.2014.04.008 10.1016/j.difgeo.2016.03.011 10.1007/s00220-014-1911-6 10.1070/SM1970v010n03ABEH001677 10.1016/j.aim.2014.09.011 10.1142/S0219199704001501 10.1016/j.jfa.2016.12.020 10.1016/j.jfa.2016.12.021 10.1007/s00526-016-0951-5 10.1142/S0219199711004464 10.1007/BF01245096 10.1016/j.top.2005.02.002 10.1070/SM1970v012n02ABEH000920 10.2140/pjm.2017.287.49 10.4310/jdg/1080835659 10.1016/j.jfa.2018.04.008 10.1090/tran/7196 10.1007/s00526-016-1070-z 10.1090/S1079-6762-05-00142-3 10.1016/j.top.2005.02.001 |
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| References | Andreev (br0020) 1970; 10 Guo (br0200) 2011; 13 Chow, Luo (br0030) 2003; 63 Ge, Jiang (br0080) Colin de Verdière (br0040) 1991; 104 Ge (br0050) 2018; 370 Zhang, Guo, Zhang, Luo, Yau, Gu (br0270) 2014; 76 Ge, Xu (br0130) 2014; 267 Ge, Xu, Zhang (br0170) 2017; 287 Ge, Jiang (br0070) 2016; 55 Ge, Jiang (br0100) 2017; 272 Ge (br0060) 2012 Hamilton (br0210) 1988; vol. 71 Ge, Xu (br0110) Ge, Xu (br0150) 2017 Glickenstein (br0180) 2005; 44 Andreev (br0010) 1970; 12 Thurston (br0260) 1976 Miller, McDonald, Alsing, Gu, Yau (br0250) 2014; 329 Zhao, Li, Ge, Lei, Zhang, Wang, Gu (br0280) 2018; vol. 63 Marden, Rodin (br0240) 1990; vol. 1435 Luo (br0230) 2005; 11 Ge, Xu (br0120) 2018; 275 Luo (br0220) 2004; 6 Ge, Jiang (br0090) 2017; 272 Ge, Xu (br0140) 2016; 55 Glickenstein (br0190) 2005; 44 Ge, Xu (br0160) 2016; 47 Guo (10.1016/j.aim.2018.05.039_br0200) 2011; 13 Ge (10.1016/j.aim.2018.05.039_br0070) 2016; 55 Luo (10.1016/j.aim.2018.05.039_br0230) 2005; 11 Andreev (10.1016/j.aim.2018.05.039_br0010) 1970; 12 Ge (10.1016/j.aim.2018.05.039_br0100) 2017; 272 Ge (10.1016/j.aim.2018.05.039_br0160) 2016; 47 Luo (10.1016/j.aim.2018.05.039_br0220) 2004; 6 Ge (10.1016/j.aim.2018.05.039_br0140) 2016; 55 Zhao (10.1016/j.aim.2018.05.039_br0280) 2018; vol. 63 Ge (10.1016/j.aim.2018.05.039_br0080) Hamilton (10.1016/j.aim.2018.05.039_br0210) 1988; vol. 71 Ge (10.1016/j.aim.2018.05.039_br0150) 2017 Miller (10.1016/j.aim.2018.05.039_br0250) 2014; 329 Andreev (10.1016/j.aim.2018.05.039_br0020) 1970; 10 Thurston (10.1016/j.aim.2018.05.039_br0260) 1976 Ge (10.1016/j.aim.2018.05.039_br0130) 2014; 267 Ge (10.1016/j.aim.2018.05.039_br0050) 2018; 370 Ge (10.1016/j.aim.2018.05.039_br0060) 2012 Glickenstein (10.1016/j.aim.2018.05.039_br0190) 2005; 44 Ge (10.1016/j.aim.2018.05.039_br0090) 2017; 272 Ge (10.1016/j.aim.2018.05.039_br0120) 2018; 275 Zhang (10.1016/j.aim.2018.05.039_br0270) 2014; 76 Chow (10.1016/j.aim.2018.05.039_br0030) 2003; 63 Ge (10.1016/j.aim.2018.05.039_br0170) 2017; 287 Ge (10.1016/j.aim.2018.05.039_br0110) Glickenstein (10.1016/j.aim.2018.05.039_br0180) 2005; 44 Marden (10.1016/j.aim.2018.05.039_br0240) 1990; vol. 1435 Colin de Verdière (10.1016/j.aim.2018.05.039_br0040) 1991; 104 |
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| Title | On combinatorial Calabi flow with hyperbolic circle patterns |
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