15 citations · 23 across the 15 of their papers we have counts for
17 papers
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…
A distance comparison principle for curve shortening flow with free boundary
Mat Langford, Jonathan J. Zhu
We introduce a reflected chord-arc profile for curves with orthogonal boundary condition and obtain a chord-arc estimate for embedded free boundary curve shortening flows in a conv…
Ancient Ricci flows of bounded girth
Theodora Bourni, Timothy Buttsworth, Ramiro Lafuente +1
For each , we construct a 'pancake-like', -invariant ancient Ricci flow with positive curvature operator and bounded "girth", and we determine its asympt…
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…
Classification of convex ancient free boundary curve shortening flows in the disc
Theodora Bourni, Mat Langford
We classify convex ancient curve shortening flows in the disc with free boundary on the circle.
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…
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…
The atomic structure of ancient grain boundaries
Theodora Bourni, Mat Langford, Giuseppe Tinaglia
Democritus and the early atomists held that "the material cause of all things that exist is the coming together of atoms and void. Atoms are eternal and have many different shapes,…
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…
On the construction of closed nonconvex nonsoliton ancient mean curvature flows
Theodora Bourni, Mathew Langford, Alexander Mramor
We construct closed, embedded, ancient mean curvature flows in each dimension with the topology of . These examples are not mean convex and not soliton…
Convex ancient solutions to mean curvature flow
Theodora Bourni, Mat Langford, Giuseppe Tinaglia
X.-J. Wang proved a series of remarkable results on the structure of convex ancient solutions to mean curvature flow. Some of his results do not appear to be widely known, however,…
Convex ancient solutions to curve shortening flow
Theodora Bourni, Mat Langford, Giuseppe Tinaglia
We show that the only convex ancient solutions to curve shortening flow are the stationary lines, shrinking circles, Grim Reapers and Angenent ovals, completing the classification…
On the existence of translating solutions of mean curvature flow in slab regions
Theodora Bourni, Mat Langford, Giuseppe Tinaglia
We prove, in all dimensions , that there exists a convex translator lying in a slab of width in (and in no smaller slab) if and only if $θ\in[0…
A collapsing ancient solution of mean curvature flow in
Theodora Bourni, Mat Langford, Giuseppe Tinaglia
We construct a compact, convex ancient solution of mean curvature flow in with symmetry that lies in a slab of width . We provide detailed as…
Type-II singularities of two-convex immersed mean curvature flow
Theodora Bourni, Mat Langford
We show that any strictly mean convex translator of dimension which admits a cylindrical estimate and a corresponding gradient estimate is rotationally symmetric. As a co…