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On the notion of general type
Published 1997-01-01“…A smooth compact manifold M is said to have negative Yamabe invariant if all the scalar curvatures of unit-volume constant-scalar-curvature riemannian metrics on M are less than some (uniform) negative constant. …”
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A note on extremal functions for sharp Sobolev inequalities
Published 2007-06-01“…In this note we prove that any compact Riemannian manifold of dimension $ngeq 4$ which is non-conformal to the standard n-sphere and has positive Yamabe invariant admits infinitely many conformal metrics with nonconstant positive scalar curvature on which the classical sharp Sobolev inequalities admit extremal functions. …”
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