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Flat minimizers of the Willmore functional: Euler-Lagrange equations
Peter HornungAbstract
Let
We prove that there exist minimizers of the Willmore functional restricted to a class of isometric immersions of the Riemannian surface
We derive the Euler-Lagrange equations satisfied by such constrained minimizers. Our main motivation comes from nonlinear elasticity, where this constrained Willmore functional arises naturally and is called Kirchhoff's plate functional.
- Received:
- 18.07.08
- Published:
- 23.07.08