Search

MiS Preprint Repository

We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint
22/2009

The Completion of the Manifold of Riemannian Metrics

Brian Clarke

Abstract

We give a description of the completion of the manifold of all smooth Riemannian metrics on a fixed smooth, closed, finite-dimensional, orientable manifold with respect to a natural metric called the $L^2$ metric. The primary motivation for studying this problem comes from Teichmüller theory, where similar considerations lead to a completion of the well-known Weil-Petersson metric. We give an application of the main theorem to the completions of Teichmüller space with respect to a class of metrics that generalize the Weil-Petersson metric.

Received:
Apr 7, 2009
Published:
Apr 9, 2009
MSC Codes:
58D17, 58B20

Related publications

inJournal
2013 Journal Open Access
Brian Clarke

The completion of the manifold of Riemannian metrics

In: Journal of differential geometry, 93 (2013) 2, pp. 203-268