71 citations · 772 across the 59 of their papers we have counts for
6 papers · 2 filters
Ricci flow on Kaehler-Einstein surfaces
Xiuxiong Chen, Gang Tian
In this paper, we construct a set of new functionals of Ricci curvature on any Kaehler manifolds which are invariant under holomorphic transfermations in Kaehler Einstein manifolds…
A new parabolic flow in Kaehler manifolds
Xiuxiong Chen
In this paper, we introduce a new parabolic equation on Kähler manifolds. The static point of this flow is related to the existence of a lower bound of the Mabuchi energy. In this…
Calabi flow in Riemann surfaces revisited: A new point of view
Xiuxiong Chen
In this paper, we observe a set of functionals of metrics which are all decrease under the Calabi flow and have uniform lower bound along the flow, which give rise to a set of inte…
Ricci flow on Kaehler manifolds
Xiuxiong Chen, Gang Tian
In this paper, we announce the following results: Let M be a Kaehler-Einstein manifold with positive scalar curvature. If the initial metric has nonnegative bisectional curvature a…
Weak Limits of Riemannian Metrics in Surfaces with integral Curvature Bound
Xiuxiong Chen
In this paper, we study the weak compactness of the set of conformal metrics in any Riemann surface without boundary whose Calabi energy and area are uniformly bounded. We prove th…
The Space of Kaehler metrics
Xiuxiong Chen
Donaldson conjectured \cite{Dona96} that the space of Kähler metrics is geodesic convex by smooth geodesic and that it is a metric space. Following Donaldson's program, we verify t…