Abstract:
Inverse problems are notoriously unstable and to stabilise them
one needs to impose some a priori conditions. In the case of anisotropic
IP or IP on manifolds, these conditions should be coordinate-invariant
involving curvature, volume growth, etc. These bring the question of
stabilizing IP into the framework of the Gromov-Cheeger theory of
geometric convergence. We discuss these issues for the case when the
imposed geometric conditions allow for the 1D collapse to orbifolds. This is a common work
with M. Lassas and T. Yamaguchi