Mean curvature flow of arbitrary co-dimensional Reifenberg sets

@article{Hershkovits2015MeanCF,
  title={Mean curvature flow of arbitrary co-dimensional Reifenberg sets},
  author={Or Hershkovits},
  journal={Calculus of Variations and Partial Differential Equations},
  year={2015},
  volume={57},
  pages={1-15}
}
We study the existence and uniqueness of smooth mean curvature flow, in arbitrary dimension and co-dimension, emanating from so called k-dimensional $$(\varepsilon ,R)$$(ε,R) Reifenberg flat sets in $$\mathbb {R}^n$$Rn. The Reifenberg condition, roughly speaking, says that the set has a weak metric notion of a k-dimensional tangent plane at every point and scale, but those tangents are allowed to tilt as the scales vary. We show that if the Reifenberg parameter $$\varepsilon $$ε is small enough… CONTINUE READING