An analytic approach to the normalized Ricci flow-like equation

摘要

This paper is concerned with a parabolic equation with a non-local term defined on a compact two-dimensional Riemannian surface. If the total mass of the solution, , is equal to 8 and is the standard sphere S2, it is a Hamilton's normalized Ricci flow. We obtain the global in time existence of the solution to this problem for 0 < 8. If 0 < < 8, the orbit is compact while for D 8, there is a time sequence along which the solution converges to a stationary solution