328 citations · 682 across the 29 of their papers we have counts for
30 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…
The Willmore problem for surfaces with symmetry
Rob Kusner, Ying Lü, Peng Wang
The Willmore Problem seeks closed surfaces in of a given topological type minimizing the squared-mean-curvature energy $W = \int |H_{\mathbb{R}^4}…
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…
Geometry of complete minimal surfaces at infinity and the Willmore index of their inversions
Jonas Hirsch, Rob Kusner, Elena Mäder-Baumdicker
We study complete minimal surfaces in with finite total curvature and embedded planar ends. After conformal compactification via inversion, these yield examples of s…
On the Canham Problem: Bending Energy Minimizers for any Genus and Isoperimetric Ratio
Robert Kusner, Peter McGrath
Building on work of Mondino-Scharrer, we show that among closed, smoothly embedded surfaces in of genus and given isoperimetric ratio , there exists one with…
On the Willmore problem for surfaces with symmetry
Rob Kusner, Peng Wang
The Willmore Problem seeks the surface in of a given topological type minimizing the squared-mean-curvature energy $W = \int |\mathbf{H}_{\mathbb{R}…