Affiliation:
1. Department of Mathematics , Johns Hopkins University , Baltimore , MD 21231 , USA
Abstract
Abstract
In this article, we extend an unknottedness theorem for compact self-shrinkers to the mean curvature flow to shrinkers with finite topology and one asymptotically conical end, which conjecturally comprises the entire set of self-shrinkers with finite topology and one end.
The mean curvature flow itself is used in the argument presented.
Reference65 articles.
1. B. Andrews,
Noncollapsing in mean-convex mean curvature flow,
Geom. Topol. 16 (2012), no. 3, 1413–1418.
2. B. Andrews, M. Langford and J. McCoy,
Non-collapsing in fully non-linear curvature flows,
Ann. Inst. H. Poincaré C Anal. Non Linéaire 30 (2013), no. 1, 23–32.
3. S. B. Angenent and J. J. L. Velázquez,
Degenerate neckpinches in mean curvature flow,
J. reine angew. Math. 482 (1997), 15–66.
4. J. Bernstein and L. Wang,
A topological property of asymptotically conical self-shrinkers of small entropy,
Duke Math. J. 166 (2017), no. 3, 403–435.
5. K. A. Brakke,
The motion of a surface by its mean curvature,
Math. Notes 20,
Princeton University, Princeton 1978.