Minimizers of the Willmore functional under fixed conformal class

Flat minimizers of the Willmore functional: Euler-Lagrange equations

Let S ⊂ R be a bounded C domain and let g denote the flat metric in R. 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. We derive the Euler-Lagrange equations satisfied by such constrained minimizers. Our main motivation comes from nonlinear elasticity, where this constrained Willmore functiona...

Existence of Minimizing Willmore Surfaces of Prescribed Conformal Class

Mathematik in den Naturwissenschaften Leipzig Regularity results for flat minimizers of the Willmore functional

Let S ⊂ R2 be a bounded domain with boundary of class C∞ and let gij = δij denote the flat metric on R 2. Let u be a minimizer of the Willmore functional within a subclass (defined by prescribing boundary conditions on parts of ∂S) of all W 2,2 isometric immersions of the Riemannian manifold (S, g) into R3. In this article we study the regularity properties of such u. Our main result roughly st...

The Willmore Functional on Lagrangian Tori: Its Relation to Area and Existence of Smooth Minimizers

In this paper we prove an existence and regularity theorem for la-grangian tori minimizing the Willmore functional in Euclidean four-space, R4 ,with the standard metric and symplectic structure. Technical difficulties arisebecause the Euler-Lagrange equation for this problem is a sixth-order nonlinearpartial differential equation. This research was motivated by a study of the<lb...

the effect of functional/notional approach on the proficiency level of efl learners and its evaluation through functional test

in fact, this study focused on the following questions: 1. is there any difference between the effect of functional/notional approach and the structural approaches to language teaching on the proficiency test of efl learners? 2. can a rather innovative language test referred to as "functional test" ge devised so so to measure the proficiency test of efl learners, and thus be as much reliable an...