https://neckpinch.com/authors/yuning-liu/New arXiv papers by Yuning Liu, from Neckpinch Tue, 03 Nov 2026 07:43:57 GMT https://neckpinch.com/papers/2411.18284/arxiv:2411.18284Wed, 27 Nov 2024 00:00:00 GMTYuning Liu, Yoshihiro Tonegawa — Suppose that a closed 1-rectifiable set Γ₀⊂ℝ² of finite 1-dimensional Hausdorff measure and a vector field u in a dimensionally critical Sobolev space are given. It is proved that, starting from Γ₀, there exists a non-trivial flow of curves with the normal velocity given by the sum of the curvature and the given vector field u. The motion law is satisfied in the sense of Brakke and the flow exists through singularities.Other curvature flowsSingularitiesWeak & singular flows