The Yamabe constant on noncompact manifolds
Differential Geometry
2014-04-15 v2
Abstract
We prove several facts about the Yamabe constant of Riemannian metrics on general noncompact manifolds and about S. Kim's closely related "Yamabe constant at infinity". In particular we show that the Yamabe constant depends continuously on the Riemannian metric with respect to the fine C^2-topology, and that the Yamabe constant at infinity is even locally constant with respect to this topology. We also discuss to which extent the Yamabe constant is continuous with respect to coarser topologies on the space of Riemannian metrics.
Cite
@article{arxiv.1206.0610,
title = {The Yamabe constant on noncompact manifolds},
author = {Nadine Große and Marc Nardmann},
journal= {arXiv preprint arXiv:1206.0610},
year = {2014}
}
Comments
23 pages. Lemma 10.1, Theorem 1.2 and a few minor issues corrected