2018/05/06 by Lohkamp, Joachim
#30L99 #49Q15 #51M10 #53A10 #53A30 #Differential Geometry (math.DG) #FOS: Mathematics
paper · doi:10.48550/arxiv.1805.02180
We study the intrinsic geometry of area minimizing (and also of almost minimizing) hypersurfaces from a new point of view by relating this subject to quasiconformal geometry. For any such hypersurface we define and construct a so-called S-structure which reveals some unexpected geometric and analytic properties of the hypersurface and its singularity set. In this paper, this is used to prove the existence of hyperbolic unfoldings: canonical conformal deformations of the regular part of these hypersurfaces into complete Gromov hyperbolic spaces of bounded geometry with Gromov boundary homeomorphic to the singular set.