71 citations · 772 across the 59 of their papers we have counts for
6 papers · 1 filter
The space of volume forms
Xiuxiong Chen, Weiyong He
S. Donaldson introduced a metric on the space of volume forms, with fixed total volume on any compact Riemmanian manifold. With this metric, the space of volume forms formally has…
Space of Kähler metrics (IV)--On the lower bound of the K-energy
Xiuxiong Chen
We partially confirm an old conjecture of Donaldson that if there exists a cscK metrics in a given Kähler class, then there is no degenerated geodesic ray which is tamed by a bound…
Remarks on Kahler Ricci Flow
Xiuxiong Chen, Bing Wang
We study some estimates along the Kahler Ricci flow on Fano manifolds. Using these estimates, we show the convergence of Kahler Ricci flow directly if the -invariant of the cano…
The Calabi flow on toric Fano surface
Xiuxiong Chen, Weiyong He
We prove the longtime existence and convergence of the Calabi flow on toric Fano surfaces in a large family of Kahler classes where the class has positive extremal Hamiltonian pote…
A note on Kähler-Ricci soliton
Xiuxiong Chen, Song Sun, Gang Tian
In this note we provide a proof of the following: Any compact KRS with positive bisectional curvature is biholomorphic to the complex projective space. As a corollary, we obtain an…
Stability of Kähler-Ricci flow
Xiuxiong Chen, Haozhao Li
We prove the convergence of Kähler-Ricci flow with some small initial curvature conditions. As applications, we discuss the convergence of Kähler-Ricci flow when the complex struct…