A minimal surface with unbounded curvature
Martin Traizet
TL;DR
This paper constructs a new example of a complete minimal surface in three-dimensional space that has infinite genus, infinitely many catenoidal ends, one limit end, and unbounded Gaussian curvature.
Contribution
It introduces a minimal surface with unbounded curvature, infinite genus, and infinitely many ends, expanding the known diversity of minimal surfaces.
Findings
Constructed a complete embedded minimal surface with unbounded Gaussian curvature.
The surface has infinite genus and infinitely many catenoidal type ends.
The surface features one limit end, demonstrating complex topological and geometric properties.
Abstract
We construct a complete, embedded minimal surface in euclidean 3-space which has unbounded Gaussian curvature. It has infinite genus, infinitely many catenoidal type ends and one limit end.
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Taxonomy
TopicsGeometric Analysis and Curvature Flows · Geometry and complex manifolds · Geometric and Algebraic Topology