15 citations · 57 across the 11 of their papers we have counts for
11 papers
Scalar curvature along Ebin geodesics
Christoph Böhm, Timothy Buttsworth, Brian Clarke
Let be a smooth, compact manifold and let denote the set of Riemannian metrics on with smooth volume density . For a given , we sho…
Gaussian measures on the of space of Riemannian metrics
Brian Clarke, Dmitry Jakobson, Niky Kamran +3
We introduce Gaussian-type measures on the manifold of all metrics with a fixed volume form on a compact Riemannian manifold of dimension . For this random model we compute…
Isometries of optimal pseudo-Riemannian metrics
Brian Clarke
We give a concise proof that large classes of optimal (constant curvature or Einstein) pseudo-Riemannian metrics are maximally symmetric within their conformal class.
Conformal deformations of the Ebin metric and a generalized Calabi metric on the space of Riemannian metrics
Brian Clarke, Yanir A. Rubinstein
We consider geometries on the space of Riemannian metrics conformally equivalent to the widely studied Ebin L^2 metric. Among these we characterize a distinguished metric that can…
Ricci flow and the metric completion of the space of Kahler metrics
Brian Clarke, Yanir A. Rubinstein
We consider the space of Kahler metrics as a Riemannian submanifold of the space of Riemannian metrics, and study the associated submanifold geometry. In particular, we show that t…
Geodesics, distance, and the CAT(0) property for the manifold of Riemannian metrics
Brian Clarke
Given a fixed closed manifold M, we exhibit an explicit formula for the distance function of the canonical L^2 Riemannian metric on the manifold of all smooth Riemannian metrics on…