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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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Construction of complete embedded self-similar surfaces under mean curvature flow. Part I.
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by Xuan Hien Nguyen PDF
Trans. Amer. Math. Soc. 361 (2009), 1683-1701 Request permission

Abstract:

We carry out the first main step towards the construction of new examples of complete embedded self-similar surfaces under mean curvature flow. An approximate solution is obtained by taking two known examples of self-similar surfaces and desingularizing the intersection circle using an appropriately modified singly periodic Scherk surface, called the core. Using an inverse function theorem, we show that for small boundary conditions on the core, there is an embedded surface close to the core that is a solution of the equation for self-similar surfaces. This provides us with an adequate central piece to substitute for the intersection.
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Additional Information
  • Xuan Hien Nguyen
  • Affiliation: Department of Mathematics, University of Wisconsin, Madison, Wisconsin 53706
  • Address at time of publication: Department of Mathematics, Kansas State University, 138 Cardwell Hall, Manhattan, Kansas 66506
  • MR Author ID: 857138
  • Received by editor(s): September 13, 2006
  • Published electronically: November 25, 2008
  • © Copyright 2008 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Trans. Amer. Math. Soc. 361 (2009), 1683-1701
  • MSC (2000): Primary 53C44
  • DOI: https://doi.org/10.1090/S0002-9947-08-04748-X
  • MathSciNet review: 2465812