Uniqueness of tangent flows at the first singular time of embedded surface mean-curvature flow
We prove that, at each singular point of the first singular time of the mean-curvature flow of a smooth compact connected embedded surface without boundary in ℝ3, all fixed-center rescalings converge locally smoothly on compact negative-time intervals to one multiplicity-one homothetic self-shrinker flow. The limit is unique in the original ambient coordinates, including its position and axes. No mean-convexity assumption or prescribed tangent model is required.
Cite
@misc{OAI:Tangent-flow-uniqueness-2026-09-24,
author = {{OpenAI}},
title = {{Uniqueness of tangent flows at the first singular time of embedded surface mean-curvature flow}},
howpublished = {OpenAI Math Release preprint
\href{https://github.com/openai/math/blob/main/preprints/Tangent-flow-uniqueness-2026-09-24/paper.pdf}{OAI:Tangent-flow-uniqueness-2026-09-24}},
year = {2026}
}