2 problems

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Daskalopoulos–Uhlenbeck conjecture for least-gradient functions and geodesic laminations
Daskalopoulos–Uhlenbeck conjecture. For any function of locally least gradient on $\mathbf H^2$ , $\mathop{}\!\mathrm{d}u$ should be Ruelle–Sullivan for some, possibly not maximum-s…
Conjectureopengeodesic-laminations hyperbolic-geometry least-gradient-functionsarXiv posted 2 days ago
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Singular-set conjecture for locally least-gradient functions
Singular-set conjecture. Suppose that $d\geq 8$ . Then every function of locally least gradient $u:M\to\mathbf{R}$ has a singular set $S_u$ of codimension $8$ , such that on…
Conjectureopengeometric-measure-theory least-gradient-functions minimal-laminationsarXiv posted 2 days ago

Daskalopoulos–Uhlenbeck conjecture for least-gradient functions and geodesic laminations