An existence theorem for the Yamabe problem on manifolds with boundary

Details An existence theorem for the Yamabe problem on manifolds with boundary An existence theorem for the Yamabe problem on manifolds with boundary

2009-08-29

arxiv.org/abs/0908.4327v2

Mathematics

Differential Geometry

Scientific paper

Let (M,g) be a compact Riemannian manifold with boundary. We consider the problem (first studied by Escobar in 1992) of finding a conformal metric with constant scalar curvature in the interior and zero mean curvature on the boundary. Using a local test function construction, we are able to settle most cases left open by Escobar's work. Moreover, we reduce the remaining cases to the positive mass theorem.

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