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Journal of the American Mathematical Society

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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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The Willmore functional on Lagrangian tori: its relation to area and existence of smooth minimizers
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by William P. Minicozzi PDF
J. Amer. Math. Soc. 8 (1995), 761-791 Request permission

Abstract:

In this paper we prove an existence and regularity theorem for lagrangian tori minimizing the Willmore functional in Euclidean four-space, ${{\mathbf {R}}^4}$, with the standard metric and symplectic structure. Technical difficulties arise because the Euler-Lagrange equation for this problem is a sixth-order nonlinear partial differential equation. This research was motivated by a study of the seemingly unrelated Plateau problem for lagrangian tori, and in this paper we illustrate this connection.
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Additional Information
  • © Copyright 1995 American Mathematical Society
  • Journal: J. Amer. Math. Soc. 8 (1995), 761-791
  • MSC: Primary 58E12; Secondary 35J60, 49Q05, 53C42
  • DOI: https://doi.org/10.1090/S0894-0347-1995-1311825-9
  • MathSciNet review: 1311825