English

A Sobolev Poincar\'e type inequality for integral varifolds

Differential Geometry 2012-01-05 v2

Abstract

In this work a local inequality is provided which bounds the distance of an integral varifold from a multivalued plane (height) by its tilt and mean curvature. The bounds obtained for the exponents of the Lebesgue spaces involved are shown to be sharp.

Keywords

Cite

@article{arxiv.0808.3660,
  title  = {A Sobolev Poincar\'e type inequality for integral varifolds},
  author = {Ulrich Menne},
  journal= {arXiv preprint arXiv:0808.3660},
  year   = {2012}
}

Comments

v1: 27 pages, no figures; v2: replaced citations of the author's dissertation by proofs, material of sections 1 and 3 reorganised, slightly more general results in section 2, some remarks, some discussion and some references added, 40 pages, no figures

R2 v1 2026-06-21T11:14:12.685Z