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

2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/73796We 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.33 pages; 1 figureDifferential GeometryComplex Variables53A20; 58D27; 32G15Minimal surfaces with the area growth of two planes; the case of infinite symmetrytext