71 citations · 772 across the 59 of their papers we have counts for
6 papers · 1 filter
Liouville energy on a topological two sphere
XiuXiong Chen, Meijun Zhu
In this paper we shall give an analytic proof of the fact that the Liouville energy on a topological two sphere is bounded from below. Our proof does not rely on the uniformization…
Kähler Ricci flow on Fano surfaces (I)
Xiuxiong Chen, Bing Wang
We show the properties of the blowup limits of \KRf solutions on Fano surfaces if Riemannian curvature is unbounded. As an application, on every toric Fano surface, we prove that \…
The Calabi flow on Kähler surface with bounded Sobolev constant
Xiuxiong Chen, Weiyong He
We consider the formation of singularities along the Calabi flow with the assumption of the uniform Sobolev constant. In particular, on Kähler surface we show that any "maximal bub…
Test configurations and Geodesic rays
Xiuxiong Chen, Yudong Tang
For smooth test configurations, there always exist C^{1,1} geodesic rays in Kahler metric space parallel to the algebraic ray. The invariant agrees with Futaki invariant, at…
Moduli spaces of critical Riemannian metrics with L^{n/2} norm curvature bounds
Xiuxiong Chen, Brian Weber
We consider the moduli space of the extremal Kähler metrics on compact manifolds. We show that under the conditions of two-sided total volume bounds, -norm bounds on $…
On Conformally Kaehler, Einstein Manifolds
Xiuxiong Chen, Claude LeBrun, Brian Weber
We prove that any compact complex surface with positive first Chern class admits an Einstein metric which is conformally related to a Kaehler metric. The key new ingredient is the…