Peter McGrath

activity

20242026

collaborators

Showing math.DGShow all

3 papers · 1 filter

math.DG2026

Nonorientable Minimal Surfaces Embedded in the Round $4$ -sphere

Mikhail Karpukhin, Robert Kusner, Peter McGrath +1

We show that every closed, nonorientable surface can be minimally embedded in $S^{4}$ , providing in particular the first known examples of embedded, nonorientable minimal su…

math.DG2025

Large topology asymptotics for spectrally extremal minimal surfaces in $B^{3}$ and $S^{3}$

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…

math.DG2024

Embedded minimal surfaces in $S^{3}$ and $B^{3}$ 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…

Nonorientable Minimal Surfaces Embedded in the Round 4-sphere

Large topology asymptotics for spectrally extremal minimal surfaces in B3 and S3

Embedded minimal surfaces in S3 and B3 via equivariant eigenvalue optimization

Nonorientable Minimal Surfaces Embedded in the Round $4$ -sphere

Large topology asymptotics for spectrally extremal minimal surfaces in $B^{3}$ and $S^{3}$

Embedded minimal surfaces in $S^{3}$ and $B^{3}$ via equivariant eigenvalue optimization