The evolution of H-surfaces with a Plateau boundary condition
arXiv:1308.1931 · doi:10.1016/j.anihpc.2013.10.003
Abstract
In this paper we consider the heat flow associated to the classical Plateau problem for surfaces of prescribed mean curvature. We show that an isoperimetric condition on H ensures the existence of a global weak solution. Moreover, we establish that these global solutions sub-converge, as time tends to infinity, to a conformal solution of the classical Plateau problem for surfaces of prescribed mean curvature.