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Journal of the American Mathematical Society

Published by the American Mathematical Society, the Journal of the American Mathematical Society (JAMS) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6834 (online) ISSN 0894-0347 (print)

The 2020 MCQ for Journal of the American Mathematical Society is 4.79.

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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 PDF
J. Amer. Math. Soc. 20 (2007), 441-465 Request permission

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
  • 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