3 citations · 9 across the 7 of their papers we have counts for
7 papers
Compact Hermitian surfaces with pointwise constant Gauduchon holomorphic sectional curvature
Haojie Chen, Xiaolan Nie
Motivated by a recent work of Chen-Zheng [8] on Strominger space forms, we prove that a compact Hermitian surface with pointwise constant holomorphic sectional curvature with respe…
Schwarz lemma: the case of equality and an extension
Haojie Chen, Xiaolan Nie
We prove two results related to the Schwarz lemma in complex geometry. First, we show that if the inequality in the Schwarz lemmata of Yau, Royden and Tosatti becomes equality at o…
Second order estimates for fully nonlinear elliptic equations with gradient terms on Hermitian manifolds
Bo Guan, Xiaolan Nie
We derive a priori second order estimates for fully nonlinear elliptic equations which depend on the gradients of solutions in critical ways on Hermitian manifolds. The global esti…
Chern-Ricci curvatures, holomorphic sectional curvature and Hermitian metrics
Haojie Chen, Lingling Chen, Xiaolan Nie
We present some formulae related to the Chern-Ricci curvatures and scalar curvatures of special Hermitian metrics. We prove that a compact locally conformal Kähler manifold with co…
Weak Solutions of the Chern-Ricci flow on compact complex surfaces
Xiaolan Nie
In this note, we prove the existence of weak solutions of the Chern-Ricci flow through blow downs of exceptional curves, as well as backwards smooth convergence away from the excep…
Regularity of A Complex Monge-Ampère Equation on Hermitian Manifolds
Xiaolan Nie
We obtain higher order estimates for a parabolic flow on a compact Hermitian manifold. As an application, we prove that a bounded -plurisubharmonic solution of an elliptic c…
Odd type generalized complex structures on 4-manifolds
Haojie Chen, Xiaolan Nie
We prove that a compact smooth 4-manifold admits generalized complex structures of odd type if and only if it has a transversely holomorphic 2-foliation. Consequently, there exist…