A gradient flow for the prescribed Gaussian curvature problem on a closed Riemann surface with conical singularity

摘要

In this note, we prove that the abstract gradient flow introduced byBaird-Fardoun-Regbaoui cite{BFR}is well-posed on a closed Riemann surface withconical singularity. Long time existence and convergence of the flow are provedunder certain assumptions. As an application, the prescribed Gaussian curvatureproblem is solved when the singular Euler characteristic of the conical surfaceis non-positive.