3 citations · 4 across the 9 of their papers we have counts for
13 papers
On the Areas of Genus Zero Free Boundary Minimal Surfaces Embedded in the Unit -ball
Peter McGrath, Jiahua Zou
We prove that the area of each nonflat genus zero free boundary minimal surface embedded in the unit -ball is less than the area of its radial projection to . The…
Free Boundary Minimal Annuli Immersed in the Unit 3-Ball
Nikolaos Kapouleas, Peter McGrath
Using the linearized doubling methodology we carry out a PDE gluing construction of a discrete family of non-rotational properly immersed free boundary minimal annuli in the Euclid…
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 Steklov Eigenspaces for Free Boundary Minimal Surfaces in the Unit Ball
Robert Kusner, Peter McGrath
We develop new methods to compare the span of the coordinate functions on a free boundary minimal submanifold embedded in the unit -ball with…
Symmetry and Isoperimetry for Riemannian Surfaces
Joseph Ansel Hoisington, Peter McGrath
For a domain in a geodesically convex surface, we introduce a scattering energy , which measures the asymmetry of by quantifying its incompatibility with an…
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…