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arXiv · 1309.1348

Gaussian measures on the of space of Riemannian metrics

Brian Clarke·Dmitry Jakobson·Niky Kamran·Lior Silberman·Jonathan Taylor·Yaiza Canzani
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Abstract

We introduce Gaussian-type measures on the manifold of all metrics with a fixed volume form on a compact Riemannian manifold of dimension $\geq 3$. 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.

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Brian Clarke, Dmitry Jakobson, Niky Kamran, Lior Silberman, Jonathan Taylor, Yaiza Canzani. 2015-09-06. Gaussian measures on the of space of Riemannian metrics. https://arxiv.org/abs/1309.1348

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