Journal of the American Mathematical Society

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

Author(s): William H. Meeks III; Michael Wolf
Journal: J. Amer. Math. Soc. 20 (2007), 441-465.
MSC (2000): Primary 53A10; Secondary 32G15
Posted: July 11, 2006
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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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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: 10.1090/S0894-0347-06-00537-6
PII: S 0894-0347(06)00537-6
Received by editor(s): March 10, 2005
Posted: 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
Copyright of article: Copyright 2006, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

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ISSN: 1088-6834(e) ISSN: 0894-0347(p)

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