Someone told me that it is possible to solve the Yamabe problem using Ricci flow. The proof I know of is the one originally proposed by Yamabe and then completed by Trudinger, Aubin and Schoen (in particular, the final step by Schoen made use of the positive mass theorem which had earlier been proved by Schoen and Yau).

If the Ricci flow proof exists, could someone point me to a reference?

Edit: When I say the 'Ricci flow' proof, I actually mean the Yamabe flow, since the two coincide on surfaces.