We construct Gaussian measure on the manifold of Riemannian metrics with the fixed volume form. We show that diameter and Laplace eigenvalue and volume entropy functionals are all integrable with respect to our measures. We also compute the characteristic function for the L2 (Ebin) distance from a random metric to the reference metric.
This is joint work with Y. Canzani, B. Clarke, N. Kamran, L. Silberman and J. Taylor.
This video is part of the Institute for Advanced Study‘s Symplectic geometry seminar.
