2 problems

Let $M$ be the manifold under consideration, and let $u:M\to S^1$ be an $\infty$-harmonic map in a fixed homotopy class. Uniqueness conjecture. The map $u$ is unique up to rotation…

Let $(M,g)$ be a Riemannian manifold, and consider $\infty$-harmonic functions and the associated notions of viscosity solutions, comparison with cones, gradient estimates, and reg…