We work in PDE-constrained shape optimization as well as the analysis of shape spaces, which are infinite-dimensional Riemannian manifolds. For instance, we prove existence and regularity of shortest ...

[1] E.J. Beggs and S. Majid, Quantum Riemannian Geometry, Grundlehren der mathematischen Wissenschaften, vol. 355, Springer (2020) 809pp. [2] J. Argota-Quiroz and S. Majid, Quantum gravity on finite ...