We give a self-contained treatment of set-theoretic subsolutions to flow by mean curvature, or, more generally, to flow by mean curvature plus an ambient vector field. The ambient space can be any smooth Riemannian manifold. Most importantly, we show that if two such set-theoretic subsolutions are initially disjoint, then they remain disjoint provided one of the subsolutions is compact; previously, this was only known for Euclidean space (with no ambient vectorfield). We also give a simple proof of a version of Ilmanen’s interpolation theorem.
All Science Journal Classification (ASJC) codes
- Statistics and Probability
- Geometry and Topology
- Statistics, Probability and Uncertainty