Minimal surfaces with the area growth of two planes; the case of infinite symmetry
William H. Meeks, Michael Wolf
Abstract
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 2πR2 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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