A version of Allard's rectifiability theorem with explicit bounds is given. The condition on the mean curvature would correspond to a bound in Sobolev spaces with fractional negative exponents.
Cite this article
Stephan Luckhaus, Uniform Rectifiability from Mean Curvature Bounds. Z. Anal. Anwend. 27 (2008), no. 4, pp. 451–461DOI 10.4171/ZAA/1364