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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- Masahiro Yamada, Master thesis, Department of Mathematics and Information Sciences, Tokyo Metropolitan University, 2018 (Japanese).
- 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
- MR Author ID: 899165
- Email: firstname.lastname@example.org
- 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.
- © Copyright 2019 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 372 (2019), 7597-7617
- MSC (2010): Primary 53C44; Secondary 52C26
- DOI: https://doi.org/10.1090/tran/7778
- MathSciNet review: 4029675