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math.DG2021
Quadratically pinched submanifolds of the sphere via mean curvature flow with surgery
Mat Langford, Stephen Lynch, Huy The Nguyen
We study mean curvature flow of -dimensional submanifolds of , the round -sphere of sectional curvature , under the quadratic curvature pinching con…
math.DG2021
Collapsing and noncollapsing in convex ancient mean curvature flow
Theodora Bourni, Mat Langford, Stephen Lynch
We provide several characterisations of collapsing and noncollapsing in convex ancient mean curvature flow, establishing in particular that collapsing occurs if and only if the flo…
math.DG2021
Uniqueness of convex ancient solutions to hypersurface flows
Stephen Lynch
We show that every convex ancient solution of mean curvature flow with Type I curvature growth is either spherical, cylindrical, or planar. We then prove the corresponding statemen…