Uniform ball property and existence of optimal shapes for a wide class of geometric functionals
Uniform ball property and existence of optimal shapes for a wide class of geometric functionals
In this article, we study shape optimization problems involving the geometry of surfaces (normal vector, principal curvatures). Given \varepsilon > 0 and a fixed non-empty large bounded open hold-all B \subset \mathbb{R}^{n} , n \geqslant 2 , we consider a specific class \mathcal{O}_{\varepsilon}(B) of open sets \Omega \subset B satisfying …