Shahid Bahonar University of Kerman Journal of Mahani Mathematical Research 2251-7952 13 1 2023 11 01 Ricci-Bourguignon flow on an open surface 159 165 3762 10.22103/jmmr.2023.20469.1358 EN Shahroud Azami Department of Pure Mathematics, Faculty of Science, Imam Khomeini International University, Qazvin, Iran. Journal Article 2022 10 30 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 https://jmmrc.uk.ac.ir/article_3762_3af8710c7d81f7bcb8ac23ed0c799774.pdf