Abstract
We study the Yamabe invariant of manifolds which admit metrics of positive scalar curvature. Analysing `best Sobolev constants'we give a technique to find positive lower bounds for the invariant.We apply these ideas to show that for any compact Riemannian manifold (N n,g) of positive scalarcurvature there is a positive constant K =K(N, g), which depends only on (N, g), such that for any compact manifold M m, the Yamabe invariantof M m × N nis no less than K times the invariant ofS n + m. We will find some estimates for the constant K in the case N =S n.
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Petean, J. Best Sobolev Constants and Manifolds with Positive Scalar Curvature Metrics. Annals of Global Analysis and Geometry 20, 231–242 (2001). https://doi.org/10.1023/A:1012037030262
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DOI: https://doi.org/10.1023/A:1012037030262