Mathematical analysis proves the existence of forced curvature flows for 1-rectifiable initial data, indicating robust geometric curve evolution through singularities.
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.
No takes yet. Share an insight, caveat, or question.
Liu et al. (2026) studied this question.
Synapse has enriched 5 closely related papers on similar clinical questions. Consider them for comparative context: