O funcional de Willmore e sua invariância conforme.

Abstract

In the paper, we study the Willmore funcional for a differentiable, closed and orientable surface S, moreover, we prove the invariance of this functional under conformal transformations of Euclidean space R3. To achieve these objectives, we first explain some concepts and preliminary, deemed necessary, to understand the main content of the paper. After this explanation, we will define the Willmore functional and we will show some properties about this functional, among them, the invariance under conformal transformations of R3. And per finally, we will present two generalizations for this functional. This first, is the Willmore functional of dimension n, while the second is the Willmore functional relative to an Riemannian manifold M n (n ≥ 3) and we will prove that the latter generalization is invariant under conformal changes of the metric.