In this article, we extend the mean curvature flow with surgery to mean convex
hypersurfaces with entropy less than Λ n-2. In particular, 2-convexity is not assumed. Next …

We prove a strong Frankel theorem for mean curvature flow shrinkers in all dimensions: Any
two shrinkers in a sufficiently large ball must intersect. In particular, the shrinker itself must …

Self-shrinkers are basic singularity models for the mean curvature flow, and, in the
noncompact case, nongeneric ones (generic ones being generalized round cylinders Sk. p …

Brakke flow is defined with a variational inequality, which means it may have discontinuous
mass over time, ie have mass drop. It has long been conjectured that the Brakke flow …

In this thesis, we derive various entropy upper bounds for self-shrinkers of the mean
curvature flow which admit a symmetry, including several applications. In our first paper …

In this article we prove an unknottedness result for self shrinkers in $\mathbb {R}^ 3$ with
multiple asymptotically conical ends which bound a handlebody in a natural sense, using …