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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

The conformal Yamabe constant of product manifolds


Authors: Bernd Ammann, Mattias Dahl and Emmanuel Humbert
Journal: Proc. Amer. Math. Soc. 141 (2013), 295-307
MSC (2010): Primary 35J60; Secondary 35P30, 58J50, 58C40
Published electronically: May 23, 2012
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Abstract: Let $ (V,g)$ and $ (W,h)$ be compact Riemannian manifolds of dimension at least $ 3$. We derive a lower bound for the conformal Yamabe constant of the product manifold $ ( V \times W, g+h)$ in terms of the conformal Yamabe constants of $ (V,g)$ and $ (W,h)$.


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Additional Information

Bernd Ammann
Affiliation: Fakultät für Mathematik, Universität Regensburg, 93040 Regensburg, Germany
Email: bernd.ammann@mathematik.uni-regensburg.de

Mattias Dahl
Affiliation: Institutionen för Matematik, Kungliga Tekniska Högskolan, 100 44 Stockholm, Sweden
Email: dahl@math.kth.se

Emmanuel Humbert
Affiliation: Institut Élie Cartan, BP 239, Université de Nancy 1, 54506 Vandoeuvre-lès-Nancy Cedex, France
Address at time of publication: Laboratoire de Mathématiques et Physique Théorique, Université de Tours, Parc de Grandmot, 37200 Tours, France
Email: emmanuel.humbert@lmpt.univ-tours.fr

DOI: http://dx.doi.org/10.1090/S0002-9939-2012-11320-6
PII: S 0002-9939(2012)11320-6
Keywords: Yamabe constant, Yamabe invariant, product manifolds
Received by editor(s): March 9, 2011
Received by editor(s) in revised form: June 22, 2011
Published electronically: May 23, 2012
Additional Notes: The first author was partially supported by DFG Sachbeihilfe AM 144/2-1.
The second author was partially supported by the Swedish Research Council.
The third author was partially supported by ANR-10-BLAN 0105.
Communicated by: Michael Wolf
Article copyright: © Copyright 2012 American Mathematical Society