I presume you are referring to the <A HREF="https://en.wikipedia.org/wiki/Yamabe_flow">Yamabe flow</A> approach to the <A HREF="https://en.wikipedia.org/wiki/Yamabe_problem">Yamabe problem</A>, which in 2 dimensions reduces to a Ricci flow. Relevant references include - <A HREF="https://math.stackexchange.com/questions/762693/request-for-online-reference-to-hamiltons-the-ricci-flow-on-surfaces">The Ricci flow on surfaces</A> (1988) - <A HREF="https://projecteuclid.org/euclid.jdg/1214446319">The Ricci flow on the 2-sphere</A> (1991) - <A HREF="https://onlinelibrary.wiley.com/doi/abs/10.1002/cpa.3160450805">The Yamabe flow on locally conformally flat manifolds with positive Ricci curvature</A> (1992) - <A HREF="https://projecteuclid.org/euclid.jdg/1214454674">Global existence and convergence of Yamabe flow</A> (1994)