2015/07/09 by Alexander Lytchak, Stefan Wenger, Lytchak, Alexander +1 · 3 citations
Mathematics · #49Q05 #52A38 #Differential Geometry (math.DG) #FOS: Mathematics #Metric Geometry (math.MG) #math.DG #math.MG #msc:49Q05 #msc:52A38
paper · pdf · doi:10.48550/arxiv.1507.02670
typos corrected, references updated
arxiv created 2015/07/16 · arxiv updated 2015/07/17
We show that in the setting of proper metric spaces one obtains a solution of the classical two-dimensional Plateau problem by minimizing the energy, as in the classical case, once a definition of area (in the sense of convex geometry) has been chosen appropriately. We prove the quasi-convexity of this new definition of area. Under the assumption of a quadratic isoperimetric inequality we establish regularity results for energy minimizers and improve Hoelder exponents of some area-minimizing discs.