Minimal laminations and level sets of 1-harmonic functions
Analysis of PDEs
2024-07-26 v2 Differential Geometry
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 -harmonic) iff its level sets are a minimal lamination; this resolves an open problem of Daskalopoulos and Uhlenbeck.
Keywords
Cite
@article{arxiv.2311.01541,
title = {Minimal laminations and level sets of 1-harmonic functions},
author = {Aidan Backus},
journal= {arXiv preprint arXiv:2311.01541},
year = {2024}
}
Comments
32 pages. Revised according to comments of referee. To appear in Journal of Geometric Analysis. Comments welcome