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Article Dans Une Revue Communications in Analysis and Geometry Année : 2013

Square-integrability of solutions of the Yamabe equation

Résumé

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 our paper [4]. As an application we see that the smooth Yamabe invariant of any two-connected compact seven-dimensional manifold is at least 74.5. Similar conclusions follow in dimension 8 and in dimensions >= 11.

Dates et versions

hal-01282157 , version 1 (03-03-2016)

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Bernd Ammann, Mattias Dahl, Emmanuel Humbert. Square-integrability of solutions of the Yamabe equation. Communications in Analysis and Geometry, 2013, 21 (5), pp.891-916. ⟨10.4310/CAG.2013.v21.n5.a2⟩. ⟨hal-01282157⟩
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