The authors show that the 2-non-negative traceless bisectional curvature is preserved along the Khler-Ricci flow. The positivity of Ricci curvature is also preserved along the Khler-Ricci flow with 2-non-negative ...The authors show that the 2-non-negative traceless bisectional curvature is preserved along the Khler-Ricci flow. The positivity of Ricci curvature is also preserved along the Khler-Ricci flow with 2-non-negative traceless bisectional curvature. As a corollary, the Khler-Ricci flow with 2-non-negative traceless bisectional curvature will converge to a Khler-Ricci soliton in the sense of Cheeger-Gromov-Hausdorff topology if complex dimension n ≥ 3.展开更多
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 theorem and the Onofri inequality,thu...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 theorem and the Onofri inequality,thus it is essentially needed in the alternative proof of the uniformization theorem via the Calabi flow.Such an analytic approach also sheds light on how to obtain the boundedness for E1 energy in the study of general Kähler manifolds.展开更多
In this paper, we consider the complex Monge-Ampère equation posed on a compact Kahler manifold. We show how to get L^p(p < ∞) and L^∞ estimates for the gradient of the solution in terms of the continuity of...In this paper, we consider the complex Monge-Ampère equation posed on a compact Kahler manifold. We show how to get L^p(p < ∞) and L^∞ estimates for the gradient of the solution in terms of the continuity of the right-hand side.展开更多
基金the National Science Foundation (No. DMS-0406346)
文摘The authors show that the 2-non-negative traceless bisectional curvature is preserved along the Khler-Ricci flow. The positivity of Ricci curvature is also preserved along the Khler-Ricci flow with 2-non-negative traceless bisectional curvature. As a corollary, the Khler-Ricci flow with 2-non-negative traceless bisectional curvature will converge to a Khler-Ricci soliton in the sense of Cheeger-Gromov-Hausdorff topology if complex dimension n ≥ 3.
基金We thank Yuxiang Li for pointing out the proof of Lemma 3.5 in an early version is incomplete.We also thank the referee for the careful reviewing and comments.
文摘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 theorem and the Onofri inequality,thus it is essentially needed in the alternative proof of the uniformization theorem via the Calabi flow.Such an analytic approach also sheds light on how to obtain the boundedness for E1 energy in the study of general Kähler manifolds.
基金supported by National Science Foundation of USA(Grant No.DMS1914719)
文摘In this paper, we consider the complex Monge-Ampère equation posed on a compact Kahler manifold. We show how to get L^p(p < ∞) and L^∞ estimates for the gradient of the solution in terms of the continuity of the right-hand side.
