Minimal surfaces with the area growth of two planes; the case of infinite symmetry

Details Minimal surfaces with the area growth of two planes; the case of infinite symmetry Minimal surfaces with the area growth of two planes; the case of infinite symmetry

2005-01-08

arxiv.org/abs/math/0501110v1

Mathematics

Differential Geometry

33 pages; 1 figure

Scientific paper

We prove that a connected properly immersed minimal surface in Euclidean 3-space with infinite symmetry group whose intersection with a ball of radius R is less than 2\piR^2 is a plane, a catenoid or a Scherk singly-periodic minimal surface. In particular, we prove that the only periodic minimal desingularization of a pair of intersecting planes is Scherk's singly-periodic minimal surface.

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