Answers are grounded in this paper and cite their sources.
The study demonstrates that short density-drop theorem and multiplicity-one theorem suffice to resolve Huisken's conjecture, highlighting advancements in mean curvature flow theory.
Bamler–Kleiner recently proved a multiplicity-one theorem for mean curvature flow in <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:msup> <m:mi mathvariant="double-struck">R</m:mi> <m:mn>3</m:mn> </m:msup> </m:math> R³ and combined it with the authors’ work on generic mean curvature flows to fully resolve Huisken’s genericity conjecture. In this paper, we show that a short density-drop theorem plus the Bamler–Kleiner multiplicity-one theorem for tangent flows at the first nongeneric singular time suffice to resolve Huisken’s conjecture – without relying on the strict genus-drop theorem for one-sided ancient flows previously established by the authors.
No takes yet. Share an insight, caveat, or question.
Chodosh et al. (2025) studied this question.
Synapse has enriched 10 related papers. Consider them for comparative context: