An existence theorem on the isoperimetric ratio over scalar-flat conformal classes

@article{Chen2020AnET,
  title={An existence theorem on the isoperimetric ratio over scalar-flat conformal classes},
  author={Xuezhang Chen and Tianling Jin and Yuping Ruan},
  journal={Journal of Differential Equations},
  year={2020}
}
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References

SHOWING 1-10 OF 18 REFERENCES
On the isoperimetric quotient over scalar-flat conformal classes
Abstract Let (M, g) be a smooth compact Riemannian manifold of dimension n with smooth boundary . Suppose that (M, g) admits a scalar-flat conformal metric. We prove that the supremum of the…
The Han-Li conjecture in constant scalar curvature and constant boundary mean curvature problem on compact manifolds
Conformal deformations to scalar-flat metrics with constant mean curvature on the boundary
Let (M, g) be a compact manifold with nonempty boundary and finite Sobolev quotient Q(M, ∂M). We prove that there exists a conformal deformation which is scalar-flat and has constant boundary mean…
Conformal deformation of a Riemannian metric to a scalar flat metric with constant mean curvature on the boundary
One of the most celebrated theorems in mathematics is the Riemann mapping theorem. It says that an open, simply connected, proper subset of the plane is conformally diffeomorphic to the disk. In…
Conformal Deformation to Scalar Flat Metrics with Constant Mean Curvature on the Boundary in Higher Dimensions
In 1992, motivated by Riemann mapping theorem, Escobar considered a version of Yamabe problem on manifolds of dimension n greater than 2 with boundary. The problem consists in finding a conformal…
Conformal deformation of a Riemannian metric to constant scalar curvature
A well-known open question in differential geometry is the question of whether a given compact Riemannian manifold is necessarily conformally equivalent to one of constant scalar curvature. This…
The existence of conformal metrics with constant scalar curvature and constant boundary mean curvature
Let (M,g) be an n dimensional compact, smooth, Riemannian manifold without boundary. For n = 2, the Uniformization Theorem of Poincare says that there exist metrics on M which are pointwise conformal…
An extension operator on bounded domains and applications
In this paper we study a sharp Hardy–Littlewood–Sobolev type inequality with Riesz potential on bounded smooth domains. We obtain the inequality for a general bounded domain $$\Omega $$Ω and show…
An integral equation in conformal geometry
Existence results for the Yamabe problem on manifolds with boundary
Given a compact Riemannian manifold with umbilic boundary, we prove the existence of conformally related metrics of zero scalar curvature and constant mean curvature on the boundary, under suitable…
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