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

2017/06/26 by Yunyan Yang, Yang, Yunyan
Mathematics · #Geometric Analysis and Curvature Flows #Nonlinear Partial Differential Equations #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.1706.08237

Abstract

In this note, we prove that the abstract gradient flow introduced by Baird-Fardoun-Regbaoui \citeBFRis well-posed on a closed Riemann surface with conical singularity. Long time existence and convergence of the flow are proved under certain assumptions. As an application, the prescribed Gaussian curvature problem is solved when the singular Euler characteristic of the conical surface is non-positive.

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