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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Bibliographic Details
Published inAdvances in mathematics (New York. 1965) Vol. 333; pp. 523 - 538
Main Authors Ge, Huabin, Hua, Bobo
Format Journal Article
LanguageEnglish
Published Elsevier Inc 31.07.2018
Subjects
Calabi flow
Circle patterns
Hyperbolic geometry
Hyperbolic geometry
Circle patterns
Calabi flow
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ISSN0001-8708
1090-2082
DOI10.1016/j.aim.2018.05.039

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Summary: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.
ISSN:0001-8708
1090-2082
DOI:10.1016/j.aim.2018.05.039