3 papers
math.DG2024
New minimal surface doublings of the Clifford torus and contributions to questions of Yau
Nikolaos Kapouleas, Peter McGrath
The purpose of this article is three-fold. First, we apply a general theorem from our earlier work to produce many new minimal doublings of the Clifford Torus in the round three-sp…
math.DG2024
Embedded minimal surfaces in and via equivariant eigenvalue optimization
Mikhail Karpukhin, Robert Kusner, Peter McGrath +1
In 1970, Lawson solved the topological realization problem for minimal surfaces in the sphere, showing that any closed orientable surface can be minimally embedded in $\mathbb{S}^3…
math.DG2016
Rotational Symmetry of Asymptotically Conical Mean Curvature Flow Self-Expanders
Frederick Tsz-Ho Fong, Peter McGrath
In this article, we examine complete, mean-convex self-expanders for the mean curvature flow whose ends have decaying principal curvatures. We prove a Liouville-type theorem associ…