MiS Preprint Repository

Delve into the future of research at MiS with our preprint repository. Our scientists are making groundbreaking discoveries and sharing their latest findings before they are published. Explore repository to stay up-to-date on the newest developments and breakthroughs.

MiS Preprint

Flat minimizers of the Willmore functional: Euler-Lagrange equations

Peter Hornung


Let $S\subset R^2$ be a bounded $C^1$ domain and let $g$ denote the flat metric in $R^2$.

We prove that there exist minimizers of the Willmore functional restricted to a class of isometric immersions of the Riemannian surface $(S, g)$ into $R^3$.

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.

Jul 18, 2008
Jul 23, 2008

Related publications

2008 Repository Open Access
Peter Hornung

Flat minimizers of the Willmore functional : Euler-Lagrange equations