A family of curvature flows on surfaces with boundary
Let \(M\) be a compact surface with boundary. In the present paper, a family of evolution equations is constructed and it is shown that the solutions which exist for all times, converge exponentially to a metric with constant Gauss curvature in the interior and constant geodesic curvature on the boundary. The proof is based on integral estimates and uses results of \textit{X. Chen} [Int. Math. Res. Not. 2001, No. 6, 275--297 (2001; Zbl 1078.53065)] and \textit{M. Struwe} [Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) 1, 247--274 (2002; Zbl 1150.53025)].
scientific article; zbMATH DE number 1922568