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

Thumbnail Image

Date

Authors

Journal Title

Journal ISSN

Volume Title

Publisher

Abstract

Description

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.
33 pages; 1 figure

Keywords

Differential Geometry, Complex Variables, 53A20; 58D27; 32G15

Citation

URI

http://salesiana.dossiersoluciones.com/handle/123456789/73796

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0501110
 http://arxiv.org/abs/math/0501110

Collections

arXiv