Noncompactness results for Yamabe problem on manifolds with boundary

Abstract:

We study a linear perturbation of the Yamabe problem on manifolds with boundary, in particular we perturb the mean curvature term.

We show that is the perturbation has positive sign then there exists a sequence of solutions which blows up as the perturbation goes to zero.

This result holds whenever the boundary is umbilic or the boundary consists only of non umbilic points, provided the dimension of the manifold is large enough.