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arXiv · 0908.4327

An existence theorem for the Yamabe problem on manifolds with boundary

S. Brendle·S. Chen
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Abstract

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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S. Brendle, S. Chen. 2009-09-04. An existence theorem for the Yamabe problem on manifolds with boundary. https://arxiv.org/abs/0908.4327

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