Generalized Yamabe Flows

Abstract

In this work we introduce a family of conformal flows generalizing the classical Yamabe flow. We prove that for a large class of such flows long-time existence holds, and the arguments are in fact simpler than in the classical case. Moreover, we establish convergence for the case of negative scalar curvature and expect a similar statement for the positive and the flat cases as well.

V2: Added some clarification about the potential difference between the background metric and the initial metric. Corrected typos