Nadine Große, Marc Nardmann
Published 2012-06-04, updated 2012-09-27Version 2
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.
Comments: 23 pages. Lemma 10.1, Theorem 1.2 and a few minor issues corrected
Journal: Journal of Geometric Analysis 24 (2014), no. 2, 1092-1125
Topological properties of manifolds admitting a $Y^x$-Riemannian metric
The volume and lengths on a three sphere
The Riemannian L^2 topology on the manifold of Riemannian metrics
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