Suitable Spaces for Shape Optimization

Abstract The differential-geometric structure of the manifold smooth shapes is applied to theory shape optimization problems. In particular, a Riemannian gradient with respect first Sobolev metric and Steklov–Poincaré are defined. Moreover, covariant derivative associated deduced in this paper. explicit expression leads definition Hessian metric. paper, we give brief overview various techniques based on gradients Hessian. Since space limits application techniques, paper extends $$H^{1/2}$$ H 1 / 2 -shapes, which arise naturally We define diffeological new -shapes. This can be seen as step towards formulation spaces.