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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

Convergence of combinatorial Ricci flows to degenerate circle patterns


Author: Asuka Takatsu
Journal: Trans. Amer. Math. Soc.
MSC (2010): Primary 53C44; Secondary 52C26
DOI: https://doi.org/10.1090/tran/7778
Published electronically: June 10, 2019
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Abstract: We investigate the combinatorial Ricci flow on a surface of nonpositive Euler characteristic when the necessary and sufficient condition for the convergence of the combinatorial Ricci flow is not valid. This observation addresses one of the questions raised by B. Chow and F. Luo.


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Additional Information

Asuka Takatsu
Affiliation: Department of Mathematical Sciences, Tokyo Metropolitan University, Tokyo 192-0397, Japan; and Mathematical Analysis Team, RIKEN Center for Advanced Intelligence Project (AIP), Tokyo 103-0027, Japan
Email: asuka@tmu.ac.jp

DOI: https://doi.org/10.1090/tran/7778
Keywords: Weighted triangulation, circle pattern, combinatorial Ricci flow, gradient flow
Received by editor(s): September 4, 2018
Received by editor(s) in revised form: December 13, 2018
Published electronically: June 10, 2019
Additional Notes: This work was supported by JSPS KAKENHI Grants Number 15K17536, 16KT0132.
Article copyright: © Copyright 2019 American Mathematical Society