, Volume 24, Issue 2, pp 1092-1125

The Yamabe Constant on Noncompact Manifolds

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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 what extent the Yamabe constant is continuous with respect to coarser topologies on the space of Riemannian metrics.

This work was done during our joint stay at the Hausdorff Institute for Mathematics. We thank the organizers for the hospitality.