Open Access
Translator Disclaimer
2015 Ricci flow on surfaces with conic singularities
Rafe Mazzeo, Yanir Rubinstein, Natasa Sesum
Anal. PDE 8(4): 839-882 (2015). DOI: 10.2140/apde.2015.8.839


We establish short-time existence of the Ricci flow on surfaces with a finite number of conic points, all with cone angle between 0 and 2π, with cone angles remaining fixed or changing in some smooth prescribed way. For the angle-preserving flow we prove long-time existence; if the angles satisfy the Troyanov condition, this flow converges exponentially to the unique constant-curvature metric with these cone angles; if this condition fails, the conformal factor blows up at precisely one point. These geometric results rely on a new refined regularity theorem for solutions of linear parabolic equations on manifolds with conic singularities. This is proved using methods from geometric microlocal analysis, which is the main novelty of this article.


Download Citation

Rafe Mazzeo. Yanir Rubinstein. Natasa Sesum. "Ricci flow on surfaces with conic singularities." Anal. PDE 8 (4) 839 - 882, 2015.


Received: 26 May 2014; Revised: 27 January 2015; Accepted: 6 March 2015; Published: 2015
First available in Project Euclid: 16 November 2017

zbMATH: 1322.53070
MathSciNet: MR3366005
Digital Object Identifier: 10.2140/apde.2015.8.839

Primary: 53C44 , 58J35

Keywords: conic singularities , Heat kernels , Ricci flow

Rights: Copyright © 2015 Mathematical Sciences Publishers


Vol.8 • No. 4 • 2015
Back to Top