Abstract
We study the Yamabe problem in the context of manifolds with boundary - a basic problem in Riemannian geometry - from the point of view of nonlinear elliptic boundary value problems. By making good use of bifurcation theory from a simple eigenvalue, we show that nonpositive scalar curvatures and nonpositive mean curvatures are not always conformal to constant negative scalar curvatures and the zero mean curvature.
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