Moreover, measuring the wavefronts of elastic waves scattered from discontinuities inside the Earth, one obtains information on the broken geodesics in the Riemannian metric. Thus seismic measurements ...

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 ...

Quantum Riemannian geometry is a generalisation of geometry that ... many new tools which are available, such as quantum geodesics, and many more calculations that can be done even in existing models.