Ricci-Bourguignon flow on an open surface

Abstract

In this paper, we investigate the normalized Ricci-Bourguignon flow with incomplete initial metric on an open surface. We show that such a flow converges exponentially to a metric with constant Gaussian curvature if the initial metric is suitable. In particular, if the initial metric is complete then the metrics converge to the standard hyperbolic metric.

Keywords

• ricci-bourguignon flow
• incomplete surface
• uniformization theorem