In this paper,we give a survey of our recent results on extension theorems on Kähler manifolds for holomorphic sections or cohomology classes of(pluri)canonical line bundles twisted with holomorphic line bundles ...In this paper,we give a survey of our recent results on extension theorems on Kähler manifolds for holomorphic sections or cohomology classes of(pluri)canonical line bundles twisted with holomorphic line bundles equipped with singular metrics,and also discuss their applications and the ideas contained in the proofs.展开更多
The author shows that if a locally conformal K?hler metric is Hermitian YangMills with respect to itself with Einstein constant c≤0,then it is a Kahler-Einstein metric.In the case of c>0,some identities on torsion...The author shows that if a locally conformal K?hler metric is Hermitian YangMills with respect to itself with Einstein constant c≤0,then it is a Kahler-Einstein metric.In the case of c>0,some identities on torsions and an inequality on the second Chern number are derived.展开更多
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 the constant nonpositive holomorphi...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 the constant nonpositive holomorphic sectional curvature is K?hler.We also give examples of complete non-Kähler metrics with pointwise negative constant but not globally constant holomorphic sectional curvature,and complete non-Kähler metrics with zero holomorphic sectional curvature and nonvanishing curvature tensors.展开更多
We establish a new partial C^(0)-estimate along a continuity path mixed with conic singularities along a simple normal crossing divisor and a positive twisted(1,1)-form on Fano manifolds.As an application,this estimat...We establish a new partial C^(0)-estimate along a continuity path mixed with conic singularities along a simple normal crossing divisor and a positive twisted(1,1)-form on Fano manifolds.As an application,this estimate enables us to show the reductivity of the automorphism group of the limit space,which leads to a new proof of the Yau-Tian-Donaldson conjecture.展开更多
Riemannian流形和Khler流形上Laplace-Beltrami算子谱的下界的估计是微分几何研究领域的热点问题.针对LiS和Tran M A得到的关于Laplace-Beltrami算子谱的下界的估计,利用华罗庚先生和陆启铿先生关于有界对称典型域的研究结论,得出了...Riemannian流形和Khler流形上Laplace-Beltrami算子谱的下界的估计是微分几何研究领域的热点问题.针对LiS和Tran M A得到的关于Laplace-Beltrami算子谱的下界的估计,利用华罗庚先生和陆启铿先生关于有界对称典型域的研究结论,得出了第一类有界对称典型域上Laplace-Beltrami算子谱的下界估计.展开更多
基金the National Natural Science Foundation of China(11688101 and 11431013)the National Natural Science Foundation of China(12022110,11201347 and 11671306).
文摘In this paper,we give a survey of our recent results on extension theorems on Kähler manifolds for holomorphic sections or cohomology classes of(pluri)canonical line bundles twisted with holomorphic line bundles equipped with singular metrics,and also discuss their applications and the ideas contained in the proofs.
文摘The author shows that if a locally conformal K?hler metric is Hermitian YangMills with respect to itself with Einstein constant c≤0,then it is a Kahler-Einstein metric.In the case of c>0,some identities on torsions and an inequality on the second Chern number are derived.
基金supported by National Natural Science Foundation of China(Grant No.11801516)Zhejiang Provincial Natural Science Foundation(Grant No.LY19A010017)。
文摘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 the constant nonpositive holomorphic sectional curvature is K?hler.We also give examples of complete non-Kähler metrics with pointwise negative constant but not globally constant holomorphic sectional curvature,and complete non-Kähler metrics with zero holomorphic sectional curvature and nonvanishing curvature tensors.
基金supported by Le Centre de recherche en géométrie et topologie Fellowship during the visit to Institut des sciences mathématiques of Universitédu QuébecàMontréal。
文摘We establish a new partial C^(0)-estimate along a continuity path mixed with conic singularities along a simple normal crossing divisor and a positive twisted(1,1)-form on Fano manifolds.As an application,this estimate enables us to show the reductivity of the automorphism group of the limit space,which leads to a new proof of the Yau-Tian-Donaldson conjecture.
文摘Riemannian流形和Khler流形上Laplace-Beltrami算子谱的下界的估计是微分几何研究领域的热点问题.针对LiS和Tran M A得到的关于Laplace-Beltrami算子谱的下界的估计,利用华罗庚先生和陆启铿先生关于有界对称典型域的研究结论,得出了第一类有界对称典型域上Laplace-Beltrami算子谱的下界估计.
