https://neckpinch.com/authors/natasha-diederen/New arXiv papers by Natasha Diederen, from Neckpinch Tue, 03 Nov 2026 08:41:12 GMT https://neckpinch.com/papers/2610.08357/arxiv:2610.08357Tue, 06 Oct 2026 00:00:00 GMTNatasha Diederen — We construct an example of a smooth embedding of S^(p+q-1) in ℝ^(p+q) whose evolution under the mean curvature flow forms an isolated singularity at one point, after which it is a smoothly embedded copy of S^(p-1)× S^q. In doing so, we prove some general results about SO(p)× SO(q)-invariant mean curvature flow whose initial data is generated by the rotation of a graphical profile curve, including an analysis of bubblesheet singularities. The most involved part of our analysis is an instant smoothness result, which requires a delicate approximation and pseudolocality.Mean curvature flowSingularities