3 citations · 3 across the 3 of their papers we have counts for
4 papers
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…
Area Bounds for Free Boundary Minimal Surfaces in a Geodesic Ball in the Sphere
Brian Freidin, Peter McGrath
We extend to higher dimensions earlier sharp bounds for the area of two dimensional free boundary minimal surfaces contained in a geodesic ball of the round sphere. This follows wo…
Minimal Surfaces in the Round Three-Sphere by Doubling the Equatorial Two-Sphere, II
Nikolaos Kapouleas, Peter McGrath
In earlier work of NK new closed embedded smooth minimal surfaces in the round three-sphere were constructed, each resembling two parallel copies of the equatoria…
Closed Mean Curvature Self-Shrinking Surfaces of Generalized Rotational Type
Peter McGrath
For each we construct a new closed embedded mean curvature self-shrinking hypersurface in . These self-shrinkers are diffeomorphic to $S^{n-1}\times S^{n…