Family 355Differential geometryNo LeanNot yet digested
Unique tangent flows at the first surface singularity
Proves the first-singular-time case of tangent-flow uniqueness for smooth compact connected embedded surfaces without boundary in ℝ. At every singular point, all fixed-center backward tangent flows agree as area measures at every negative time in the original ambient coordinates, without mean-convexity or a prescribed tangent model.
Manuscripts in this family · 1
Uniqueness of tangent flows at the first singular time of embedded surface mean-curvature flow
·paper.pdf
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 ℝ, 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.