Stochastic Ricci Flow on Compact Surfaces

Ricci Solitons on Compact Kahler Surfaces

We classify the Kähler metrics on compact manifolds of complex dimension two that are solitons for the constant-volume Ricci flow, assuming that the curvature is slightly more positive than that of the single known example of a soliton in this dimension.

Harmonic Ricci Flow on surfaces

Let g(t) be a family of smooth Riemannian metrics on an n-dimensional closed manifold M . Moreover, given a smooth closed Riemannian manifold (N, gN ) of arbitrary dimension, let φ(t) be a family of smooth maps from M to N . Then (g(t), φ(t)) is called a solution of the volume preserving Harmonic Ricci Flow (or Ricci Flow coupled with Harmonic Map Heat Flow), if it satisfies  ∂tg = −2 Ricg + ...

Ricci Yang-mills Flow on Surfaces

Abstract. We study the behaviour of the Ricci Yang-Mills flow for U(1) bundles on surfaces. We show that existence for the flow reduces to a bound on the isoperimetric constant. In the presence of such a bound, we show that on S, if the bundle is nontrivial, the flow exists for all time. For higher genus surfaces the flow always exists for all time. The volume normalized flow always exists for ...

Normalized Ricci Flow on Nonparabolic Surfaces

This paper studies normalized Ricci flow on a nonparabolic surface, whose scalar curvature is asymptotically −1 in an integral sense. By a method initiated by R. Hamilton, the flow is shown to converge to a metric of constant scalar curvature −1. A relative estimate of Green’s function is proved as a tool.

0 Ricci flow on Kähler - Einstein surfaces