Critical Allard regularity: pointwise tilt-excess estimates
Differential Geometry
2024-02-21 v1
Abstract
The main results of this paper provide VMO-type estimates for the quadratic tilt-excess on varifolds with critical generalized mean curvature. These estimates apply to varifolds with "almost-integral" density which are close to a multiplicity one -disc in a ball in the usual senses. The class of almost-integral varifolds allows for varifolds with non-perpendicular mean curvature. Moreover, the estimates hold \emph{uniformly for every point} in a relatively open set in and naturally imply a Reifenberg-type parametrization. The proof relies upon generalizing the -valued Lipschitz approximation and Sobolev-Poincar\'e estimates of arXiv:0808.3660 to almost-integral rectifiable varifolds.
Cite
@article{arxiv.2402.12752,
title = {Critical Allard regularity: pointwise tilt-excess estimates},
author = {Sean McCurdy},
journal= {arXiv preprint arXiv:2402.12752},
year = {2024}
}