{"id":"openai-math/Tangent-flow-uniqueness-2026-09-24","pdf":"https://github.com/openai/math/blob/main/preprints/Tangent-flow-uniqueness-2026-09-24/paper.pdf","url":"https://github.com/openai/math/tree/main/preprints/Tangent-flow-uniqueness-2026-09-24","tags":["geometric-analysis","mean-curvature-flow","singularities"],"score":0,"title":"Uniqueness of tangent flows at the first singular time of embedded surface mean-curvature flow","domain":"Differential geometry","family":"355","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"math.DG","summary":"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 3 , 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.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-10-23","reactions":{},"formalized":false,"family_title":"Unique tangent flows at the first surface singularity"}