On bifurcation of solutions of the Yamabe problem in product manifolds

  • L.L. de Lima

    Departamento de Matemática, Universidade Federal do Ceará, Brazil
  • P. Piccione

    Departamento de Matemática, Universidade de São Paulo, Brazil
  • M. Zedda

    Università degli Studi di Cagliari, Italy

Abstract

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.

Cite this article

L.L. de Lima, P. Piccione, M. Zedda, On bifurcation of solutions of the Yamabe problem in product manifolds. Ann. Inst. H. Poincaré Anal. Non Linéaire 29 (2012), no. 2, pp. 261–277

DOI 10.1016/J.ANIHPC.2011.10.005