3 papers
math.AP2025
New Homogeneous Solutions for the One-Phase Free Boundary Problem
Coleman Hines, James Kolesar, Peter McGrath
For each sufficiently large integer , we construct a domain in the round -sphere with boundary components which is the link of a cone in admitting a homoge…
math.DG2024
New minimal surface doublings of the Clifford torus and contributions to questions of Yau
Nikolaos Kapouleas, Peter McGrath
The purpose of this article is three-fold. First, we apply a general theorem from our earlier work to produce many new minimal doublings of the Clifford Torus in the round three-sp…
math.DG2020
Generalizing the Linearized Doubling approach, I: General theory and new minimal surfaces and self-shrinkers
Nikolaos Kapouleas, Peter McGrath
In Part I of this article we generalize the Linearized Doubling (LD) approach, introduced in earlier work by NK, by proving a general theorem stating that if is a closed minima…