https://neckpinch.com/authors/roger-moser/New arXiv papers by Roger Moser, from Neckpinch Tue, 03 Nov 2026 08:37:45 GMT https://neckpinch.com/papers/2108.05807/arxiv:2108.05807Thu, 12 Aug 2021 00:00:00 GMTRoger Moser — Given an ∞-harmonic function u_∞ on a domain Ω⊆ ℝ², consider the function w = −log |∇u_∞|. If u_∞ ∈ C²(Ω) with ∇u_∞ ≠ 0 and ∇|∇u_∞| ≠ 0, then it is easy to check that (1) the streamlines of u_∞ are the level sets of w and (2) w solves the level set formulation of the inverse mean curvature flow. For less regular solutions, neither statement is true in general, but even so, w is still a weak solution of the inverse mean curvature flow under far weaker assumptions. This is proved through an approximation of u_∞ by p-harmonic functions, the use of conjugate p'-harmonic functions, and the known connection of the latter with the inverse mean curvature flow. A statement about the regularity of |∇u_∞| arises as a by-product.Mean curvature flowOther curvature flowsInverse mean curvature flowWeak & singular flows