The Yamabe Constant on Noncompact Manifolds |
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Authors: | Nadine Große Marc Nardmann |
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Institution: | 1.Department of Mathematics,University of Leipzig,Leipzig,Germany;2.Department of Mathematics,University of Hamburg,Hamburg,Germany |
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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. |
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