Hyperbolic Unfoldings of Minimal Hypersurfaces
Differential Geometry
2018-05-08 v1
Abstract
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.
Keywords
Cite
@article{arxiv.1805.02180,
title = {Hyperbolic Unfoldings of Minimal Hypersurfaces},
author = {Joachim Lohkamp},
journal= {arXiv preprint arXiv:1805.02180},
year = {2018}
}