1 citations · 2 across the 7 of their papers we have counts for
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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…
CMC hypersurfaces with bounded Morse index
Theodora Bourni, Ben Sharp, Giuseppe Tinaglia
We develop a bubble-compactness theory for embedded CMC hypersurfaces with bounded index and area inside closed Riemannian manifolds in low dimensions. In particular we show that c…
The vanishing of the fundamental gap of convex domains in
Theodora Bourni, Julie Clutterbuck, Xuan Hien Nguyen +3
For the Laplace operator with Dirichlet boundary conditions on convex domains in , , we prove that the product of the fundamental gap with the square of the d…
Ancient solutions for flow by powers of the curvature in
Theodora Bourni, Julie Clutterbuck, Xuan Hien Nguyen +3
We construct a new compact convex embedded ancient solution of the flow in , that lies between two parallel lines. Using this solution we class…
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…