Shahroud Azami - Department of Pure Mathematics, Faculty of Science, Imam Khomeini International University, Qazvin, Iran.

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.

Ricci-Bourguignon flow, incomplete surface, uniformization theorem