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arXiv · 1805.02180

Hyperbolic Unfoldings of Minimal Hypersurfaces

Joachim Lohkamp
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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.

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Joachim Lohkamp. 2018-05-06. Hyperbolic Unfoldings of Minimal Hypersurfaces. https://arxiv.org/abs/1805.02180

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