https://neckpinch.com/authors/brian-krummel/New arXiv papers by Brian Krummel, from Neckpinch Tue, 10 Nov 2026 04:10:28 GMT https://neckpinch.com/papers/1609.08036/arxiv:1609.08036Mon, 26 Sep 2016 00:00:00 GMTBrian Krummel — Let N be a smooth (n+l)-dimensional Riemannian manifold. We show that if V is an area-stationary union of three or more C^(1,μ) n-dimensional submanifolds-with-boundary Mₖ ⊂ N with a common boundary Γ, then Γ is smooth and each Mₖ is smooth up to Γ (real-analytic in the case N is real-analytic). This extends a previous result of the author for codimension l = 1. We additionally show that if Vₜ\_(t ∈ (−1,1)) is a Brakke flow such that each time-slice Vₜ is a union of three or more n-dimensional submanifolds-with-boundary M_(k,t) ⊂ N with a common boundary Γₜ and with parabolic C^(2+μ) regularity in time-space, then \Γₜ\_(t ∈ (−1,1)) and M_(k,t)\_(t ∈ (−1,1)) are smooth (second Gevrey with real-analytic time-slices in the case N is real-analytic).Mean curvature flowWeak & singular flowsBoundaries & non-compactFree boundary & capillaryMinimal & CMC surfaces