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We consider the product of a compact Riemannian manifold without boundary andnull scalar curvature with a compact Riemannian manifold with boundary, nullscalar curvature and constant mean curvature on the boundary. We usebifurcation theory to prove the existence of a infinite number of conformalclasses with at least two non-homothetic Riemannian metrics of null scalarcurvature and constant mean curvature of the boundary on the product manifold.

Bifurcation results for the Yamabe problem on Riemannian manifolds with boundary