Alec J Payne

Journal Article Mathematische Annalen · June 1, 2021 We construct embedded ancient solutions to mean curvature flow related to certain classes of unstable minimal hypersurfaces in Rn+1 for n≥ 2. These provide examples of mean convex yet nonconvex ancient solutions that are not solitons, meaning that they do ... Full text Cite

Mass Drop and Multiplicity in Mean Curvature Flow

Journal Article · September 29, 2020 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 associated to a nonfattening level set flow has no mass drop and achieves equ ... Link to item Cite

Warped tori with almost non-negative scalar curvature

Journal Article Geometriae Dedicata · June 2019 Full text Cite

Nonconvex Surfaces which Flow to Round Points

Journal Article · January 9, 2019 In this article, we extend Huisken's theorem that convex surfaces flow to round points by mean curvature flow. We construct certain classes of mean convex and non-mean convex hypersurfaces that shrink to round points and use these constructions to create p ... Link to item Cite