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Square-integrability of solutions of the Yamabe equation

Ammann, Bernd and Dahl, Mattias and Humbert, Emmanuel (2011) Square-integrability of solutions of the Yamabe equation. Preprintreihe der Fakultät Mathematik 34/2011, Working Paper.

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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 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.

Item Type:Monograph (Working Paper)
Institutions: Mathematics > Prof. Dr. Bernd Ammann
Classification:
NotationType
35J60MSC
35P30MSC
57R65MSC
58J50MSC
58C40MSC
Keywords:Yamabe invariant, surgery, Lp-L2 implication
Subjects:500 Science > 510 Mathematics
Status:Unknown
Refereed:No, this version has not been refereed yet (as with preprints)
Created at the University of Regensburg:Yes
Owner:Universitätsbibliothek Regensburg
Deposited On:19 Dec 2011 11:07
Last Modified:20 Dec 2011 12:59
Item ID:23001
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