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Square-integrability of solutions of the Yamabe equation

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Ammann, Bernd ; Dahl, Mattias ; Humbert, Emmanuel
Date of publication of this fulltext: 19 Dec 2011 10:07


We show that solutions of the Yamabe equation on certain n-
dimensional non-compact Riemannian manifolds which are bounded and Lp for
p = 2n=(n-2) are also L2. This Lp-L2-implication provides explicit constants
in the surgery-monotonicity formula for the smooth Yamabe invariant in our
article [1]. 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 � 11.

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