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Journal of the American Mathematical Society
Journal of the American Mathematical Society
ISSN 1088-6834(online) ISSN 0894-0347(print)

 

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


Authors: William H. Meeks III and Michael Wolf
Journal: J. Amer. Math. Soc. 20 (2007), 441-465
MSC (2000): Primary 53A10; Secondary 32G15
Published electronically: July 11, 2006
MathSciNet review: 2276776
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Abstract: We prove that a connected properly immersed minimal surface in $ {\mathbb{E}}^3$ with infinite symmetry group and area growth constant less than $ 3\pi$ is a plane, a catenoid, or a Scherk singly-periodic minimal surface. As a consequence, the Scherk minimal surfaces are the only connected periodic minimal desingularizations of the intersections of two planes.


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Additional Information

William H. Meeks III
Affiliation: Department of Mathematics, University of Massachusetts, Amherst, Massachusetts 01003

Michael Wolf
Affiliation: Department of Mathematics, Rice University, Houston, Texas 77005

DOI: http://dx.doi.org/10.1090/S0894-0347-06-00537-6
PII: S 0894-0347(06)00537-6
Received by editor(s): March 10, 2005
Published electronically: July 11, 2006
Additional Notes: The first author was partially supported by NSF grant DMS-0405836
The second author was partially supported by NSF grants DMS-9971563 and DMS-0139887
Any opinions, findings, and conclusions or recommendations expressed in this publication are those of the authors and do not necessarily reflect the views of the NSF
Article copyright: © Copyright 2006 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.