scholarly journals On real bisectional curvature for Hermitian manifolds

2018 ◽  
Vol 371 (4) ◽  
pp. 2703-2718 ◽  
Author(s):  
Xiaokui Yang ◽  
Fangyang Zheng
Keyword(s):  
Bisectional Curvature ◽  
Hermitian Manifolds

scholarly journals Harmonic and holomorphic 1-forms on compact balanced Hermitian manifolds

2001 ◽  
Vol 14 (1) ◽  
pp. 79-93 ◽  
Author(s):  
Georgi Ganchev ◽  
Stefan Ivanov
Keyword(s):  
Hermitian Manifolds

Bounded properties of curvatures of perturbed Ricci metric on curve moduli

2014 ◽  
Vol 25 (12) ◽  
pp. 1450113
Author(s):  
Xiaorui Zhu
Keyword(s):  
Finite Volume ◽  
Ricci Curvature ◽  
Moduli Space ◽  
Point Of View ◽  
Bisectional Curvature ◽  
Bounded Geometry ◽  
Holomorphic Bisectional Curvature ◽  
Chern Form ◽  
Thick Part ◽  
Kahler Metric

As is well-known, the Weil–Petersson metric ωWP on the moduli space ℳg has negative Ricci curvature. Hence, its negative first Chern form defines the so-called Ricci metric ωτ. Their combination [Formula: see text], C > 0, introduced by Liu–Sun–Yau, is called the perturbed Ricci metric. It is a complete Kähler metric with finite volume. Furthermore, it has bounded geometry. In this paper, we investigate the finiteness of this new metric from another point of view. More precisely, we will prove in the thick part of ℳg, the holomorphic bisectional curvature of [Formula: see text] is bounded by a constant depending only on the thick constant and C0 when C ≥ (3g - 3)C0, but not on the genus g.

Weak solutions of the Monge–Ampère equation on compact Hermitian manifolds

2017 ◽  
Vol 28 (09) ◽  
pp. 1740002
Author(s):  
Sławomir Kołodziej
Keyword(s):  
Weak Solutions ◽  
A Priori Estimates ◽  
A Priori ◽  
Stability Of Solutions ◽  
Hermitian Manifolds ◽  
Priori Estimates ◽  
Existence And Stability ◽  
Monge Ampere

In this paper, we describe how pluripotential methods can be applied to study weak solutions of the complex Monge–Ampère equation on compact Hermitian manifolds. We indicate the differences between Kähler and non-Kähler setting. The results include a priori estimates, existence and stability of solutions.

scholarly journals Ricci flow on compact Kähler manifolds of positive bisectional curvature

2003 ◽  
Vol 337 (12) ◽  
pp. 781-784 ◽  
Author(s):  
Huai-Dong Cao ◽  
Bing-Long Chen ◽  
Xi-Ping Zhu
Keyword(s):  
Ricci Flow ◽  
Kähler Manifolds ◽  
Kahler Manifolds ◽  
Bisectional Curvature ◽  
Positive Bisectional Curvature
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