Ammann, Bernd, Dahl, Mattias und Humbert, Emmanuel
Square-integrability of solutions of the Yamabe equation.
Preprintreihe der Fakultät Mathematik 34/2011,
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 . 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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