Minimal laminations and level sets of 1-harmonic functions (Q6611175)

This paper investigates the regularity of minimal laminations and the convergence modes for sequences of minimal laminations. The main theorem shows that under certain curvature bounds, a lamination can be reconstructed from its set of leaves with controlled flow boxes in the Lipschitz and tangentially \(C^\infty\) sense.\N\NThis theory is then applied to give a characterization of minimal laminations: a function has a locally least gradient, i.e. is 1-harmonic, if and only if its level sets form a minimal lamination. This connects the geometric properties of laminations with the analytic properties of functions of least gradient and resolves an open problem raised by \textit{G. Daskalopoulos} and \textit{K. Uhlenbeck} [J. Differ. Geom. 127, No. 3, 969--1018 (2024; Zbl 07902275)].\N\NFinally, a compactness theorem is given: it is shown that sequences of minimal laminations with bounded curvature have convergent subsequences in various modes of convergence.