3 papers
math.DG2022★ 1 cited
Uniqueness of Asymptotically Conical Gradient Shrinking Solitons in G_2-Laplacian Flow
Mark Haskins, Ilyas Khan, Alec Payne
We prove a uniqueness result for asymptotically conical (AC) gradient shrinking solitons for the Laplacian flow of closed G_2-structures: If two gradient shrinking solitons to Lapl…
math.DG2020
Mass Drop and Multiplicity in Mean Curvature Flow
Alec Payne
Brakke flow is defined with a variational inequality, which means it may have discontinuous mass over time, i.e. have mass drop. It has long been conjectured that the Brakke flow a…
math.DG2019
Ancient and Eternal Solutions to Mean Curvature Flow from Minimal Surfaces
Alexander Mramor, Alec Payne
We construct embedded ancient solutions to mean curvature flow related to certain classes of unstable minimal hypersurfaces in for . These provide exam…