Geodesic
An existence theorem for the Yamabe problem on manifolds with boundary
Journal of the European Mathematical Society, Tome 16 (2014) no. 5, pp. 991-1016

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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.
DOI : 10.4171/jems/453
Classification : 53-XX, 00-XX, 35-XX
Keywords: Yamabe problem, manifolds with boundary 
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     author = {Simon Brendle and Szu-Yu Sophie Chen},
     title = {An existence theorem for the {Yamabe} problem on manifolds with boundary},
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Simon Brendle; Szu-Yu Sophie Chen. An existence theorem for the Yamabe problem on manifolds with boundary. Journal of the European Mathematical Society, Tome 16 (2014) no. 5, pp. 991-1016. doi: 10.4171/jems/453

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