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Square-integrability of solutions of the Yamabe equation
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).ORCID iD: 0000-0002-9184-1467
2013 (English)In: Communications in analysis and geometry, ISSN 1019-8385, E-ISSN 1944-9992, Vol. 21, no 5, 891-916 p.Article in journal (Refereed) Published
Abstract [en]

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 [4]. 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.
Keyword [en]
Scalar Curvature, Spin Cobordism, Manifolds, Invariant, Surgery
National Category
Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-140381DOI: 10.4310/CAG.2013.v21.n5.a2ISI: 000328958800002Scopus ID: 2-s2.0-84891876569OAI: oai:DiVA.org:kth-140381DiVA: diva2:690314
Funder
Swedish Research Council
Note

QC 20140123

Available from: 2014-01-23 Created: 2014-01-23 Last updated: 2017-12-06Bibliographically approved

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Dahl, Mattias

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