The Willmore functional on Lagrangian tori: its relation to area and existence of smooth minimizers

Author:
William P. Minicozzi

Journal:
J. Amer. Math. Soc. **8** (1995), 761-791

MSC:
Primary 58E12; Secondary 35J60, 49Q05, 53C42

MathSciNet review:
1311825

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Abstract: In this paper we prove an existence and regularity theorem for lagrangian tori minimizing the Willmore functional in Euclidean four-space, , 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

DOI:
https://doi.org/10.1090/S0894-0347-1995-1311825-9

Article copyright:
© Copyright 1995
American Mathematical Society