The level set flow of a hypersurface in R-4 of low entropy does not disconnect

摘要

We show that if Sigma subset of R-4 is a closed, connected hypersurface with entropy lambda(Sigma) <= lambda(S-2 x R), then the level set flow of Sigma never disconnects. We also obtain a sharp version of the forward clearing out lemma for non-fattening flows in R-4 of low entropy.