Minimal surfaces with the area growth of two planes: The case of infinite symmetry
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- by William H. Meeks III and Michael Wolf
- J. Amer. Math. Soc. 20 (2007), 441-465
- DOI: https://doi.org/10.1090/S0894-0347-06-00537-6
- Published electronically: 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.References
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Bibliographic Information
- William H. Meeks III
- Affiliation: Department of Mathematics, University of Massachusetts, Amherst, Massachusetts 01003
- MR Author ID: 122920
- Michael Wolf
- Affiliation: Department of Mathematics, Rice University, Houston, Texas 77005
- MR Author ID: 184085
- 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 - © Copyright 2006
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: J. Amer. Math. Soc. 20 (2007), 441-465
- MSC (2000): Primary 53A10; Secondary 32G15
- DOI: https://doi.org/10.1090/S0894-0347-06-00537-6
- MathSciNet review: 2276776