An existence theorem for the Yamabe problem on manifolds with boundary
By S. Brendle, S. Chen. 2009
106 citations recorded by the source corpus.
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.
Subfields: Applied Mathematics, Computational Theory and Mathematics, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/5311853d37c6a336509e75b689053c5984c8b3ae
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In Applied Mathematics
- Jun-cheng Wei
- Monica Musso
- Seunghye Kim
- Manuel del Pino
- Angela Pistoia
- A. Malchiodi
- Shusen Yan
- M. Grossi
In Computational Theory and Mathematics
- Jun-cheng Wei
- Monica Musso
- Seunghye Kim
- Manuel del Pino
- Angela Pistoia
- A. Malchiodi
- M. Grossi
- Shusen Yan
In Mathematical Physics
- Monica Musso
- Jun-cheng Wei
- Seunghye Kim
- Manuel del Pino
- Zhi-Qiang Wang
- Angela Pistoia
- Shuangjie Peng
- M. Kowalczyk
Citations in the corpus
- Existence theorems of the fractional Yamabe problem (2016, background): “f boundary Yamabe problem also suggested by Escobar [15]: Find a conformal metric such that the scalar curvature of X is constant and the boundary M is minimal. It was further studied by Brendle-Chen [5]. 2 In [10] (see also [9]), Chang and Gonza´lez observed that the fractional conformal Laplacian,”