13 citations · 14 across the 8 of their papers we have counts for
9 papers
Generic boundary behavior of Dirichlet eigenfunctions
Alec Payne, Zihui Zhao
We extend Uhlenbeck's classical results on the generic properties of Laplacian eigenfunctions. In particular, we find a residual set of domains in , , su…
The Spacetime Positive Mass Theorem with Multiple Time Dimensions
Sven Hirsch, Alec Payne, Yiyue Zhang
We generalize the spacetime positive mass theorem to include multiple time dimensions. In particular, we show that the mass remains nonnegative in the sense that the energy is…
A parabolic flow for the large volume heterotic system
Mario Garcia-Fernandez, Andres J. Moreno, Alec Payne +1
We introduce a geometric flow of conformally coclosed -structures, whose fixed points are large volume solutions of the heterotic system, with vanishing scalar torsion c…
An Intersection Principle for Mean Curvature Flow
Tang-Kai Lee, Alec Payne
The avoidance principle says that mean curvature flows of hypersurfaces remain disjoint if they are disjoint at the initial time. We prove several generalizations of the avoidance…
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…
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…
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…
Nonconvex Surfaces which Flow to Round Points
Alexander Mramor, Alec Payne
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 hyper…
Warped Tori with Almost Non-Negative Scalar Curvature
Brian Allen, Lisandra Hernandez-Vazquez, Davide Parise +2
For sequences of warped product metrics on a -torus satisfying the scalar curvature bound , uniform upper volume and diameter bounds, and a uniform lower…