Square-integrability of solutions of the Yamabe equation
by
Bernd Ammann, Mattias Dahl, Emmanuel Humbert


Square-integrability of solutions of the Yamabe equation (.dvi, .ps,.ps.gz or .pdf)
Commun. Anal. Geom. 21, 891-916 (2013)
http://dx.doi.org/10.4310/CAG.2013.v21.n5.a2

Abstract

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 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 ≥ 11.
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The Paper was written on 11.11.2011
Last update 9.1.2014