... ahigher order flow in conformal geometry By Simon Brendle1. IntroductionAn important problem in conformal geometry is the construction of con-formal metrics for which a certain curvature quantity ... the Sobolev inequality, we obtain |wk|≤C. Thus, we conclude thatSn|P0wk|2dV0≤ C.Therefore, the sequence wkis uniformly bounded in Hn.Princeton University, Princeton, NJE-mail ... Calabi flow in Riemann surfaces revisited: a new point of view, Internat. Math.Res. Notices (2001), no. 6, 275–297.GLOBAL EXISTENCE 343[7] X. Chen and G. Tian, Ricci flow on K¨ahler-Einstein surfaces,...