Xuezhang Chen

activity

20172019

most citedEscobar-Yamabe compactifications for Poincare-Einstein manifolds and rigidity theorems

3 citations · 3 across the 2 of their papers we have counts for

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math.DG2019

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

Xuezhang Chen, Tianling Jin, Yuping Ruan

Let $(M, g)$ be a smooth compact Riemannian manifold of dimension $n$ with smooth boundary $\partial M$ , admitting a scalar-flat conformal metric. We prove that the supremum of the…

math.DG2019

Blow-up phenomena for the constant scalar curvature and constant boundary mean curvature equation

Xuezhang Chen, Nan Wu

We first present a warped product manifold with boundary to show the non-uniqueness of the positive constant scalar curvature and positive constant boundary mean curvature equation…

math.DG2019

The Obata equation with Robin boundary condition

Xuezhang Chen, Mijia Lai, Fang Wang

We study the Obata equation with Robin boundary condition $\frac{\partial f}{\partial ν} + a f = 0$ on manifolds with boundary, where $a \in R ∖ {0}$ . Dirichlet and Neu…

math.DG2018

The Han-Li conjecture in constant scalar curvature and constant boundary mean curvature problem on compact manifolds

Xuezhang Chen, Yuping Ruan, Liming Sun

The Han-Li conjecture states that: Let $(M, g_{0})$ be an $n$ -dimensional $(n \geq 3)$ smooth compact Riemannian manifold with boundary having positive (generalized) Yamabe constant an…

math.DG2017★ 3 cited

Escobar-Yamabe compactifications for Poincare-Einstein manifolds and rigidity theorems

Xuezhang Chen, Mijia Lai, Fang Wang

Let $(X^{n}, g_{+})$ $(n \geq 3)$ be a Poincaré-Einstein manifold which is $C^{3, α}$ conformally compact with conformal infinity $(\partial X, [g^])$ . On the conformal compactifi…