An existence theorem of conformal scalar-flat metrics on manifolds with boundary

By S. Almaraz. 2009

81 citations recorded by the source corpus.

Let (M,g) be a compact Riemannian manifold with boundary. This paper addresses the Yamabe-type problem of finding a conformal scalar-flat metric on M, which has the boundary as a constant mean curvature hypersurface. When the boundary is umbilic, we prove an existence theorem that finishes some remaining cases of this problem.

View Paper: https://www.semanticscholar.org/paper/13ce82e969758e22aa1657181254c6077cf0b515

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1. Jun-cheng Wei
2. Monica Musso
3. Seunghye Kim
4. Manuel del Pino
5. Shuangjie Peng
6. Angela Pistoia
7. A. Malchiodi
8. Thomas Bartsch

Citations in the corpus

• Existence theorems of the fractional Yamabe problem (2016, methodology): “(3) It is notable that 4+ 2γ ∈ N andγ ∈ (0, 1) if and only ifγ = 1/2, and the boundary Yamabe problem for n = 4+ 2γ = 5 was studied in [1].”