Prescribing the boundary geodesic curvature on a compact scalar-flat Riemann surface via a flow method

Hong Zhang

Vol. 273 (2015), No. 2, 307–330

DOI: 10.2140/pjm.2015.273.307

Abstract

We study the problem of prescribing the boundary geodesic curvature on a compact scalar-flat Riemann surface. We use the negative gradient flow method. We prove the global existence and the convergence of the flow as time goes to infinity under sufficient conditions on the prescribed function.

Keywords

prescribed geodesic curvature, negative gradient flow

Mathematical Subject Classification 2010

Primary: 53C44

Secondary: 35J65

Milestones

Received: 19 November 2013

Revised: 30 July 2014

Accepted: 31 July 2014

Published: 23 December 2014