2015/01/29 by Melanie Rupflin, Rupflin, Melanie
Mathematics · #53A10 #53C44 #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #math.AP #math.DG #msc:53A10 #msc:53C44
paper · pdf · doi:10.48550/arxiv.1501.07552
Updated version with minor changes (typos corrected, Corollary 3.8 added)
arxiv created 2015/03/05 · arxiv updated 2015/03/06
We define a geometric flow that is designed to change surfaces of cylindrical type spanning two disjoint boundary curves into solutions of the Douglas-Plateau problem of finding minimal surfaces with given boundary curves. We prove that also in this new setting and for arbitrary initial data, solutions of the Teichmüller harmonic map flow exist for all times. Furthermore, for solutions for which a three-point-condition does not degenerate as t→∞, we show convergence along a sequence ti→∞ to a critical point of the area given either by a minimal cylinder or by two minimal discs spanning the given boundary curves.