JournalsjemsVol. 16, No. 5pp. 991–1016

An existence theorem for the Yamabe problem on manifolds with boundary

  • Simon Brendle

    Columbia University, New York, United States
  • Szu-Yu Sophie Chen

    Princeton University, USA
An existence theorem for the Yamabe problem on manifolds with boundary cover
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Abstract

Let (M,g)(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.

Cite this article

Simon Brendle, Szu-Yu Sophie Chen, An existence theorem for the Yamabe problem on manifolds with boundary. J. Eur. Math. Soc. 16 (2014), no. 5, pp. 991–1016

DOI 10.4171/JEMS/453