English

Ricci flow on surfaces with cusps

Differential Geometry 2009-05-11 v4

Abstract

We consider the normalized Ricci flow \deltg=(ρR)g\del_t g = (\rho - R)g with initial condition a complete metric g0g_0 on an open surface MM where MM is conformal to a punctured compact Riemann surface and g0g_0 has ends which are asymptotic to hyperbolic cusps. We prove that when χ(M)<0\chi(M) < 0 and ρ<0\rho < 0, the flow g(t)g(t) converges exponentially to the unique complete metric of constant Gauss curvature ρ\rho in the conformal class.

Keywords

Cite

@article{arxiv.math/0703357,
  title  = {Ricci flow on surfaces with cusps},
  author = {Lizhen Ji and Rafe Mazzeo and Natasa Sesum},
  journal= {arXiv preprint arXiv:math/0703357},
  year   = {2009}
}