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

Simon Brendle; Szu-Yu Sophie Chen

Journal of the European Mathematical Society (2014)

- Volume: 016, Issue: 5, page 991-1016
- ISSN: 1435-9855

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topBrendle, Simon, and Chen, Szu-Yu Sophie. "An existence theorem for the Yamabe problem on manifolds with boundary." Journal of the European Mathematical Society 016.5 (2014): 991-1016. <http://eudml.org/doc/277346>.

@article{Brendle2014,

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.},

author = {Brendle, Simon, Chen, Szu-Yu Sophie},

journal = {Journal of the European Mathematical Society},

keywords = {Yamabe problem; manifolds with boundary; positive mass theorem; Yamabe problem; manifolds with boundary; positive mass theorem},

language = {eng},

number = {5},

pages = {991-1016},

publisher = {European Mathematical Society Publishing House},

title = {An existence theorem for the Yamabe problem on manifolds with boundary},

url = {http://eudml.org/doc/277346},

volume = {016},

year = {2014},

}

TY - JOUR

AU - Brendle, Simon

AU - Chen, Szu-Yu Sophie

TI - An existence theorem for the Yamabe problem on manifolds with boundary

JO - Journal of the European Mathematical Society

PY - 2014

PB - European Mathematical Society Publishing House

VL - 016

IS - 5

SP - 991

EP - 1016

AB - 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.

LA - eng

KW - Yamabe problem; manifolds with boundary; positive mass theorem; Yamabe problem; manifolds with boundary; positive mass theorem

UR - http://eudml.org/doc/277346

ER -

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