Square-integrability of solutions of the Yamabe equation

Details Square-integrability of solutions of the Yamabe equation Square-integrability of solutions of the Yamabe equation

2011-11-11

arxiv.org/abs/1111.2780v1

Mathematics

Differential Geometry

Scientific paper

We show that solutions of the Yamabe equation on certain n-dimensional non-compact Riemannian manifolds which are bounded and L^p for p=2n/(n-2) are also L^2. This L^p-L^2-implication provides explicit constants in the surgery-monotonicity formula for the smooth Yamabe invariant in a previous article of the authors. As an application we see that the smooth Yamabe invariant of any 2-connected compact 7-dimensional manifold is at least 74.5. Similar conclusions follow in dimension 8 and in dimensions at least 11.

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