Minimal laminations and level sets of 1-harmonic functions

Abstract

We collect several results concerning regularity of minimal laminations, and governing the various modes of convergence for sequences of minimal laminations. We then apply this theory to prove that a function has locally least gradient (is $1$-harmonic) iff its level sets are a minimal lamination; this resolves an open problem of Daskalopoulos and Uhlenbeck.

32 pages. Revised according to comments of referee. To appear in Journal of Geometric Analysis. Comments welcome