MiS Preprint Repository

We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV ( that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

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.


Related publications

2008 Repository Open Access
Peter Hornung

Flat minimizers of the Willmore functional : Euler-Lagrange equations