JournalscmhVol. 87, No. 2pp. 463–475

Smooth compactness of self-shrinkers

  • Tobias H. Colding

    New York University, USA
  • William P. Minicozzi II

    The Johns Hopkins University, Baltimore, United States
Smooth compactness of   self-shrinkers cover
Download PDF


We prove a smooth compactness theorem for the space of embedded self-shrinkers in R3\mathbb{R}^3. Since self-shrinkers model singularities in mean curvature flow, this theorem can be thought of as a compactness result for the space of all singularities and it plays an important role in studying generic mean curvature flow.

Cite this article

Tobias H. Colding, William P. Minicozzi II, Smooth compactness of self-shrinkers. Comment. Math. Helv. 87 (2012), no. 2, pp. 463–475

DOI 10.4171/CMH/260