1 citations · 2 across the 8 of their papers we have counts for
8 papers
-Laplacian flow on complete asymptotically conical manifolds
Ilyas Khan
This paper proves the short-time existence of -Laplacian flow for closed, asymptotically conical -structures on a complete manifold, shows that this solution is unique am…
Uniqueness of Asymptotically Conical Gradient Shrinking Solitons in G_2-Laplacian Flow
Mark 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 Lapl…
Nonconvex ancient solutions to Curve Shortening Flow
Yongzhe Zhang, Connor Olson, Ilyas Khan +1
We construct an ancient solution to planar curve shortening. The solution is at all times compact and embedded. For it is approximated by the rotating Yin-Yang soliton, tru…
The Structure of Translating Surfaces with Finite Total Curvature
Ilyas Khan
In this paper, we prove that any mean curvature flow translator with finite total curvature and one end must be a plane. We also prove that if the transl…
Uniqueness of Asymptotically Conical Higher Codimension Self-Shrinkers and Self-Expanders
Ilyas Khan
Let be an -dimensional cone immersed in . In this paper, we show that if is a properly immersed mean curvature flow se…
Dyadic decomposition of convex domains of finite type and applications
Chun Gan, Bingyang Hu, Ilyas Khan
In this paper, we introduce a dyadic structure on convex domains of finite type via the so-called dyadic flow tents. This dyadic structure allows us to establish weighted norm esti…