Avoidance for set-theoretic solutions of mean-curvature-type flows

Or Hershkovits, Brian White

Research output: Contribution to journalArticlepeer-review

3 Scopus citations


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.

Original languageAmerican English
Pages (from-to)31-67
Number of pages37
JournalCommunications in Analysis and Geometry
Issue number1
StatePublished - 21 Sep 2023

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