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The inverse mean curvature flow perpendicular to the sphere

Differential Geometry 2016-03-09 v1 Analysis of PDEs

Abstract

We consider the smooth inverse mean curvature flow of strictly convex hypersurfaces with boundary embedded in Rn+1,\mathbb{R}^{n+1}, which are perpendicular to the unit sphere from the inside. We prove that the flow hypersurfaces converge to the embedding of a flat disk in the norm of C1,β,C^{1,\beta}, β<1.\beta<1.

Keywords

Cite

@article{arxiv.1410.5359,
  title  = {The inverse mean curvature flow perpendicular to the sphere},
  author = {Ben Lambert and Julian Scheuer},
  journal= {arXiv preprint arXiv:1410.5359},
  year   = {2016}
}

Comments

18 pages. Comments or suggestions are welcome