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Sharp distance comparison for curve shortening flow on the round sphere
Paul Bryan, Mat Langford, Jonathan J. Zhu
We prove that curve shortening flow on the round sphere displays sharp chord-arc improvement, precisely as in the planar setting (Andrews and Bryan, Comm. Anal. Geom., 2011). As in…
Ancient pancake solutions to fully nonlinear curvature flows
Sathya Rengaswami, Mat Langford
We construct -invariant ancient ``pancake'' solutions to a large and natural class of fully nonlinear curvature flows. We then establish that these are the unique…
Hamilton's Theorem (on the compactness of pinched hypersurfaces) via mean curvature flow
Theodora Bourni, Mat Langford, Stephen Lynch
We make rigorous an old idea of using mean curvature flow to prove a theorem of Richard Hamilton on the compactness of proper hypersurfaces with pinched, bounded curvature.
Classification of convex ancient free boundary mean curvature flows in the ball
Theodora Bourni, Mat Langford
We prove that there exists, in every dimension, a unique (modulo rotations about the origin and time translations) convex ancient mean curvature flow in the ball with free boundary…
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…
Differential Harnack inequalities via Concavity of the arrival time
Theodora Bourni, Mat Langford
We present a simple connection between differential Harnack inequalities for hypersurface flows and natural concavity properties of their time-of-arrival functions. We prove these…