A Note On Free Boundary Minimal Annulus
Shuangqi Liu, Zuhuan Yu
TL;DR
This paper proves that the only free boundary minimal annulus in Euclidean 3-space is the critical catenoid, using holomorphic techniques developed by Fraser and Schoen.
Contribution
It establishes the uniqueness of the free boundary minimal annulus as the critical catenoid in Euclidean 3-space.
Findings
The free boundary minimal annulus is the critical catenoid.
Holomorphic techniques can be used to classify free boundary minimal surfaces.
The result confirms the critical catenoid as the unique free boundary minimal annulus.
Abstract
In this note we investigate free boundary minimal surfaces in the Euclidean 3-space, and by using holomorphic techniques developed by Fraser and Schoen we prove that the free boundary minimal annulus is the critical catenoid.
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Taxonomy
TopicsGeometric Analysis and Curvature Flows · Point processes and geometric inequalities · Geometry and complex manifolds