SQUARE-INTEGRABILITY OF SOLUTIONS OF THE YAMABE EQUATION
Bernd Ammann, Mattias Dahl, Emmanuel Humbert · University of Regensburg Publication Server (University of Regensburg) · 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 [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.