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A note on balance equations for doubly periodic minimal surfaces
Peter Connor
Most known examples of doubly periodic minimal surfaces in with parallel ends limit as a foliation of by horizontal noded planes, with the location of…
A vase of catenoids
Peter Connor
In this note we construct a vase of catenoids - a symmetric immersed minimal surface with planar and catenoid ends.
An end-to-end construction of doubly periodic minimal surfaces
Peter Connor, Kevin Li
Using Traizet's regeneration method, we prove that for each positive integer n there is a family of embedded, doubly periodic minimal surfaces with parallel ends in Euclidean space…
A note on special polynomials and minimal surfaces
Peter Connor
When using Traizet's regeneration technique to construct minimal surfaces, the simplest nontrivial configurations are given as the roots of polynomials that satisfy a hypergeometri…
Higher genus doubly periodic minimal surfaces
Peter Connor
We construct Weierstrass data for higher genus embedded doubly periodic minimal surfaces and present numerical evidence that the associated period problem can be solved. In the ort…
Harmonic parametrization of surfaces of arbitrary genus
Peter Connor
The Weierstrass representation for minimal surfaces in provides a flexible method for constructing minimal surfaces of arbitrary genus. The topological limitations o…