14 citations · 15 across the 8 of their papers we have counts for
9 papers
Ancient solutions of Ricci flow with Type I curvature growth
Stephen Lynch, Andoni Royo Abrego
Ancient solutions of the Ricci flow arise naturally as models for singularity formation. There has been significant progress towards the classification of such solutions under natu…
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…
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…
Convexity estimates for hypersurfaces moving by concave curvature functions
Stephen Lynch
We study fully nonlinear geometric flows that deform strictly -convex hypersurfaces in Euclidean space with pointwise normal speed given by a concave function of the principal c…
Investigations on Dynamical Stability in 3D Quadrupole Ion Traps
Bogdan M. Mihalcea, Stephen Lynch
We firstly discuss classical stability for a dynamical system of two ions levitated in a 3D Radio-Frequency (RF) trap, assimilated with two coupled oscillators. We obtain the solut…
Pinched Ancient Solutions to the High Codimension Mean Curvature Flow
Stephen Lynch, Huy The Nguyen
We study solutions of high codimension mean curvature flow defined for all negative times, usually referred to as ancient solutions. We show that any compact ancient solution whose…
Sharp one-sided curvature estimates for fully nonlinear curvature flows and applications to ancient solutions
Mat Langford, Stephen Lynch
We prove several sharp one-sided pinching estimates for immersed and embedded hypersurfaces evolving by various fully nonlinear, one-homogeneous curvature flows by the method of St…
Bifurcation and Stability Analysis of Bistable Neuromodules
Stephen Lynch, Jon Borresen
This paper presents a stability analysis of simple neuromodules displaying fold bifurcations (leading to hysteresis), flip bifurcations (period doubling and undoubling to and from…