We study the problem of conformally deforming a manifold with boundary to have vanishing { \sigma}4-curvature in the interior and constant H4- curvature on the boundary. We prove that there are geometrically distinct solutions using bifurcation results proven by Case, Moreira and Wang. Surprisingly, our construction via products of a sphere and hyperbolic space only works for a finite set of dimensions.
Categories: math.DG