## 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.## References

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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