UNIFORM ESTIMATES OF SOLUTIONS OF (δ)-EQUATION ON STEIN MANIFOLDS

By means of the Hermitian metric and Chern connection, Qiu [4] obtained the Koppelman-Leray-Norguet formula for (p, q) differential forms on an open set with C1 piecewise smooth boundary on a Stein manifold, and under suitable conditions gave the solutions of (δ)-equation on a Stein manifold. In this article, using the method of Range and Siu [5], under suitable conditions, the authors complicatedly calculate to give the uniform estimates of solutions of (δ)-equation for (p, q) differential forms on a Stein manifold.     

Semistable Twisted Holomorphic Chains on Non-Compact Kähler Manifolds

In this paper, the author proves a generalized Donaldson-Uhlenbeck-Yau theorem for twisted holomorphic chain on a non-compact K\"ahler manifold. As an application, the author obtains a Bogomolov type Chern numbers inequality for semistable twisted holomorphic chain.     

追忆对陈省身的两次访谈及其他

追忆陈省身先生在他所接受的两次访谈中对中国数学界提出的殷切期望，介绍杨武之先生教书育人的事绩和成功经验．     

On the Chern‐Ricci flow and its solitons for Lie groups

This paper is concerned with Chern‐Ricci flow evolution of left‐invariant hermitian structures on Lie groups. We study the behavior of a solution, as t is approaching the first time singularity, by rescaling in order to prevent collapsing and obtain convergence in the pointed (or Cheeger‐Gromov) sense to a Chern‐Ricci soliton. We give some results on the Chern‐Ricci form and the Lie group structure of the pointed limit in terms of the starting hermitian metric and, as an application, we obtain a complete picture for the class of solvable Lie groups having a codimension one normal abelian subgroup. We have also found a Chern‐Ricci soliton hermitian metric on most of the complex surfaces which are solvmanifolds, including an unexpected shrinking soliton example.     

Analytic continuation,the Chern–Gauss–Bonnet theorem,and the Euler–Lagrange equations in Lovelock theory for indefinite signature metrics

We use analytic continuation to derive the Euler–Lagrange equations associated to the Pfaffian in indefinite signature $(p,q)$ directly from the corresponding result in the Riemannian setting. We also use analytic continuation to derive the Chern–Gauss–Bonnet theorem for pseudo-Riemannian manifolds with boundary directly from the corresponding result in the Riemannian setting. Complex metrics on the tangent bundle play a crucial role in our analysis and we obtain a version of the Chern–Gauss–Bonnet theorem in this setting for certain complex metrics.     

An Equivariant Version of the K-energy

In this note, we present a connection between equivariant Bott-Chern classes and KahlerRicci solitons. We also propose a generalized version the of the K-energy.     

The Chow ring of a singular surface

We construct the Chow ringCH*(X) =CH ⁰ (X)⊕CH ¹ (X)⊕CH ² (X) of a reduced, quasi-projective surfaceX, together with Chern class mapsc _i :K ₀ (X) → CH ⁱ (X), with the usual properties. As a consequence, we show that the cycle mapCH ² (X)→ F ₀ K ₀ (X) is an isomorphism. Our treatment is greatly influenced by an unpublished 1983 preprint of Levine’s, but is much simpler, since we deal only with surfaces.     

位形空间非定域Ward恒等式

从Faddeev Popov(FP)方法对规范理论给出的位形空间生成泛函出发，导出了位形空间非定域变换下的Ward恒等式。应用于非Abel Chern Simons(CS)理论，得到了CS规范场鬼场正规顶角间的Ward恒等，并把此结果与文献［1］做了对比，对规范理论用位形空间路径积分讨论更简便。     

Laplacian on Complex Finsler Manifolds

In this paper, the Laplacian on the holomorphic tangent bundle T1,0M of a complex manifold M endowed with a strongly pseudoconvex complex Finsler metric is defined and its explicit expression is obtained by using the Chern Finsler connection associated with (M,F). Utilizing the initiated “Bochner technique”, a vanishing theorem for vector fields on the holomorphic tangent bundle T1,0M is obtained.