Gaussian measures on the of space of Riemannian metrics

Abstract

We introduce Gaussian-type measures on the manifold of all metrics with a fixed volume form on a compact Riemannian manifold of dimension $\ge 3$. For this random model we compute the characteristic function for the $L^2$ (Ebin) distance to the reference metric. In the Appendix, we study Lipschitz-type distance between Riemannian metrics and give applications to the diameter, eigenvalue and volume entropy functionals.

arXiv comment16 pages; Final version submitted to journal per NSERC open access policy

References in corpus (1)

• Validity of the expected Euler characteristic heuristic