Combinatorial Ricci flows on surfaces

Bennett Chow, Feng Luo

Research output: Contribution to journalArticlepeer-review

193 Scopus citations

Abstract

We show that the analogue of Hamilton’s Ricci flow in the combinatorial setting produces solutions which converge exponentially fast to Thurston’s circle packing on surfaces. As a consequence, a new proof of Thurston’s existence of circle packing theorem is obtained. As another consequence, Ricci flow suggests a new algorithm to find circle packings.

Original languageEnglish (US)
Pages (from-to)97-129
Number of pages33
JournalJournal of Differential Geometry
Volume63
Issue number1
DOIs
StatePublished - 2003

All Science Journal Classification (ASJC) codes

  • Analysis
  • Algebra and Number Theory
  • Geometry and Topology

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