5 papers
Nonorientable Minimal Surfaces Embedded in the Round -sphere
Mikhail Karpukhin, Robert Kusner, Peter McGrath +1
We show that every closed, nonorientable surface can be minimally embedded in , providing in particular the first known examples of embedded, nonorientable minimal su…
Minimal surface doublings and electrostatics for Schrödinger operators
Adrian Chun-Pong Chu, Daniel Stern
Twenty years ago, N. Kapouleas introduced a singular perturbation construction known as "doubling", which produces sequences of high-genus minimal surfaces converging to a given mi…
Existence of metrics maximizing the first Laplace eigenvalue on closed surfaces
Mikhail Karpukhin, Romain Petrides, Daniel Stern
Building on seminal work of Nadirashvili and previous work of the authors, we prove the existence of metrics maximizing the area-normalized first eigenvalue of the Laplacian on eve…
Large topology asymptotics for spectrally extremal minimal surfaces in and
Mikhail Karpukhin, Peter McGrath, Daniel Stern
In recent work with Kusner, we developed a method, based on the equivariant optimization of Laplace and Steklov eigenvalues, for producing minimal surfaces of prescribed topology i…
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…