Square-integrability of solutions of the Yamabe equation
2013 (English)In: Communications in analysis and geometry, ISSN 1019-8385, Vol. 21, no 5, 891-916 p.Article in journal (Refereed) Published
We show that solutions of the Yamabe equation on certain n-dimensional non-compact Riemannian manifolds, which are bounded and L-p for p = 2n/(n -2) are also L-2. This L-p-L-2 implication provides explicit constants in the surgery-monotonicity formula for the smooth Yamabe invariant in our paper . As an application we see that the smooth Yamabe invariant of any two-connected compact seven-dimensional manifold is at least 74.5. Similar conclusions follow in dimension 8 and in dimensions >= 11.
Place, publisher, year, edition, pages
2013. Vol. 21, no 5, 891-916 p.
Scalar Curvature, Spin Cobordism, Manifolds, Invariant, Surgery
IdentifiersURN: urn:nbn:se:kth:diva-140381DOI: 10.4310/CAG.2013.v21.n5.a2ISI: 000328958800002ScopusID: 2-s2.0-84891876569OAI: oai:DiVA.org:kth-140381DiVA: diva2:690314
FunderSwedish Research Council
QC 201401232014-01-232014-01-232014-02-12Bibliographically approved