https://neckpinch.com/authors/ilyas-khan/New arXiv papers by Ilyas Khan, from Neckpinch Tue, 03 Nov 2026 08:41:12 GMT https://neckpinch.com/papers/2210.07954/arxiv:2210.07954Fri, 14 Oct 2022 00:00:00 GMTMark Haskins, Ilyas Khan, Alec Payne — We prove a uniqueness result for asymptotically conical (AC) gradient shrinking solitons for the Laplacian flow of closed G_2-structures: If two gradient shrinking solitons to Laplacian flow are asymptotic to the same closed G_2-cone, then their G_2-structures are equivalent, and in particular, the two solitons are isometric. The proof extends Kotschwar and Wang's argument for uniqueness of AC gradient shrinking Ricci solitons. We additionally show that the symmetries of the G_2-structure of an AC shrinker end are inherited from its asymptotic cone; under a mild assumption on the fundamental group, the symmetries of the asymptotic cone extend to global symmetries.Generalized & G₂ flowsRicci solitonsStability & uniquenessBoundaries & non-compact https://neckpinch.com/papers/2204.05253/arxiv:2204.05253Mon, 11 Apr 2022 00:00:00 GMTYongzhe Zhang, Connor Olson, Ilyas Khan, Sigurd Angenent — We construct an ancient solution to planar curve shortening. The solution is at all times compact and embedded. For t≪0 it is approximated by the rotating Yin-Yang soliton, truncated at a finite angle α(t) = −t, and closed off by a small copy of the Grim Reaper translating soliton.Curve shorteningAncient solutionsSelf-shrinkers & translators