The existence of conformal metrics with constant scalar curvature and constant boundary mean curvature

By Zheng-chao Han, Yanyan Li. 2000

101 citations recorded by the source corpus.

Subfields: Applied Mathematics, Astronomy and Astrophysics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/448bc602566d7215d4f931c71012f923252dde67

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

1. Yanyan Li
2. Tianling Jin
3. Jingang Xiong
4. A. Malchiodi
5. S. Almaraz
6. Z. Djadli
7. Aobing Li
8. M. Ahmedou

In Astronomy and Astrophysics

1. A. Malchiodi
2. Z. Djadli
3. O. Ahmedou
4. S. Almaraz
5. Tianling Jin
6. Yanyan Li
7. Jingang Xiong
8. Ludovic Rifford

In Geometry and Topology

1. Z. Djadli
2. Tianling Jin
3. Jingang Xiong
4. A. Malchiodi
5. Yanyan Li
6. O. Ahmedou
7. S. Almaraz
8. Aobing Li

Citations in the corpus

• Compactness results in conformal deformations of Riemannian metrics on manifolds with boundaries (2001, background): “Related problems regarding conformal deformations of Riemannian metrics on manifolds with boundaries have been studied in [1, 2, 4, 6, 9, 10, 11, 15, 16, 20, 22]; see also the references therein.”
• Estimates and existence results for a fully nonlinear Yamabe problem on manifolds with boundary (2006, background): “12) has been proved in [23, 24] under the assumption that (M, g) is of positive type and satisfies one of the following assumptions: (i) (Mn, g), n ≥ 3, is locally conformally flat with umbilic boundary; (ii) n ≥ 5 and M is not umbilical.”
• Conformal deformations to scalar-flat metrics with constant mean curvature on the boundary (2007, unknown): “Other works concerning conformal deformation on manifolds with boundary include [1], [4], [5], [8], [9], [11], [12], [13], [14] and [15].”
• Prescribing scalar and boundary mean curvature on the three dimensional half sphere (2003, methodology): “2 in [26] and standard computations, it follows that, for τ small, I ′′ τ (u) is invertible in (TvVε) , uniformly with respect to τ and v ∈ Vε.”
• An existence theorem of conformal scalar-flat metrics on manifolds with boundary (2009, background): “Other works concerning conformal deformation on manifolds with boundary include [1], [3], [5], [7], [9], [10], [12], [15], [16], [17], [18], [19] and [20].”
• A fractional Yamabe flow and some applications (2011, background): “, [23, 32, 33, 42, 43]), this fractio nal Yamabe flow (7) withσ = 1/2 is related to some generalization of Yamabe flow for manifolds w ith boundary studied in [10].”