Geodesic
On bifurcation of solutions of the Yamabe problem in product manifolds
Annales de l'I.H.P. Analyse non linéaire, Tome 29 (2012) no. 2, pp. 261-277

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We study local rigidity and multiplicity of constant scalar curvature metrics in arbitrary products of compact manifolds. Using (equivariant) bifurcation theory we determine the existence of infinitely many metrics that are accumulation points of pairwise non-homothetic solutions of the Yamabe problem. Using local rigidity and some compactness results for solutions of the Yamabe problem, we also exhibit new examples of conformal classes (with positive Yamabe constant) for which uniqueness holds.

DOI : 10.1016/j.anihpc.2011.10.005
Classification : 58E11, 58J55, 58E09 
@article{AIHPC_2012__29_2_261_0,
     author = {de Lima, L.L. and Piccione, P. and Zedda, M.},
     title = {On bifurcation of solutions of the {Yamabe} problem in product manifolds},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     pages = {261--277},
     publisher = {Elsevier},
     volume = {29},
     number = {2},
     year = {2012},
     doi = {10.1016/j.anihpc.2011.10.005},
     mrnumber = {2901197},
     zbl = {1239.58005},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1016/j.anihpc.2011.10.005/}
}
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de Lima, L.L.; Piccione, P.; Zedda, M. On bifurcation of solutions of the Yamabe problem in product manifolds. Annales de l'I.H.P. Analyse non linéaire, Tome 29 (2012) no. 2, pp. 261-277. doi: 10.1016/j.anihpc.2011.10.005

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