Blowing-up solutions for the Yamabe equation

  • Pierpaolo Esposito

    Università degli Studi "Roma Tre", Italy
  • Angela Pistoia

    Università di Roma "La Sapienza", Italy


Let be a smooth, compact Riemannian manifold of dimension . We consider the almost critical problem

where denotes the Laplace-Beltrami operator, is the scalar curvature of and is a small parameter. It is known that problem does not have any blowing-up solutions when , at least for or in the locally conformally flat case, and this is not true anymore when . Indeed, we prove that, if and the manifold is not locally conformally flat, then problem does have a family of solutions which blow-up at a maximum point of the function as Here Weyl denotes the Weyl curvature tensor of

Cite this article

Pierpaolo Esposito, Angela Pistoia, Blowing-up solutions for the Yamabe equation. Port. Math. 71 (2014), no. 3/4, pp. 249–276

DOI 10.4171/PM/1952