A gradient flow for the prescribed Gaussian curvature problem on a closed Riemann surface with conical singularity |
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Affiliation: | Department of Mathematics, Renmin University of China, Beijing 100872, PR China |
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Abstract: | In this note, we prove that the abstract gradient flow introduced by Baird-Fardoun-Regbaoui [2] is 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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Keywords: | Prescribed Gaussian curvature problem Conical singularity Gradient flow |
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