Convergence of combinatorial Ricci flows to degenerate circle patterns

Asuka Takatsu

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish
Pages (from-to)7597-7617
Number of pages21
JournalTransactions of the American Mathematical Society
Issue number11
Publication statusPublished - 2019 Dec 1
Externally publishedYes


  • Circle pattern
  • Combinatorial Ricci flow
  • Gradient flow
  • Weighted triangulation

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics


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