A Riemannian approach for PDE-constrained shape optimization over the diffeomorphism group using outer metrics

Estefania Loayza-Romero, Lidiya Pryymak, Kathrin Welker

In this paper, we study the use of outer metrics, in particular Sobolev-type metrics on the diffeomorphism group in the context of PDE-constrained shape optimization. Leveraging th…