WEIGHTED KOPPELMAN－LERAY－NORGUET FORMULAS ON A LOCAL q－CONCAVE WEDGE IN A COMPLEX MANIFOLD

A weighted Koppelman-Leray-Norguet formula of (r, s) differential forms on a local q-concave wedge in a complex manifold is obtained. By constructing the new weighted kernels, the authors give a new weighted Koppelman-Leray-Norguet formula with-out boundary integral of (r, s) differential forms, which is different from the classical one. The new weighted formula is especially suitable for the case of the local q-concave wedge with a non-smooth boundary, so one can avoid complex estimates of boundary integrals and the density of integral may be not defined on the boundary but only in the domain. Moreover, the weighted integral formulas have much freedom in applications such as in the intervolation of functions.     

BOCHNER TECHNIQUE ON STRONG KHLER-FINSLER MANIFOLDS

By using the Chern-Finsler connection and complex Finsler metric,the Bochner technique on strong Khler-Finsler manifolds is studied.For a strong Khler-Finsler manifold M,the authors first prove that there exists a system of local coordinate which is normalized at a point v ∈ M-=T 1,0M\o(M),and then the horizontal Laplace operator H for diffierential forms on PTM is defined by the horizontal part of the Chern-Finsler connection and its curvature tensor,and the horizontal Laplace operator H on holomorphic vector bundle over PTM is also defined.Finally,we get a Bochner vanishing theorem for diffierential forms on PTM.Moreover,the Bochner vanishing theorem on a holomorphic line bundle over PTM is also obtained     

Borel方向与涉及重值的亚纯函数的唯一性

利用角域Nevanlinna特征函数和亚纯函数的辐角分布理论研究了亚纯函数的角域唯一性问题,获得了一些涉及重值的角域唯一性的结果,该角域包含亚纯函数的一条Borel方向.     

A new Leray formula for smooth functions on bounded domains in Cn

By means of a new technique of integral representations in Cn given by the authors, we establish a new abstract formula with a vector function W for smooth functions on bounded domains in Cn, which is different from the well-known Leray formula, This new formula eliminates the term that contains the parameter λ from the classical Leray formula, and especially on some domains the uniform estimates for the -equation are very simple. From the new Leray formula, we can obtain correspondingly many new formulas for smooth functions on many domains in Cn, which are different from the classical ones, when we properly select the vector function W.     

闭逐块光滑流形上奇异积分的Poincaré-Bertrand公式

本文把复变函数论中著名的Poincare-Bertrand公式拓广到闭逐块C（1）光滑流形上Bochner-Martinelli型奇异积分的含有点ζ的立体角系数α（ζ）的更一般的置换公式.     

HYPERHOLOMORPHIC THEORY ON KAEHLER MANIFOLDS

First of all,using the relations (2.3),(2.4),and (2.5),we define a complex Clifford algebra Wn and the Witt basis.Secondly,we utilize the Witt basis to define the operators (6) and (6^) on Kaehler mani...     

复Finsler流形上的Koppelman-Leray公式

利用不变积分核(Berndtsson核)、复Finsler度量和联系于Chern-Finsler联络的非线性联络来研究复Finsler流形上的积分表示理论,得到了Koppelman公式和Koppelman-Leray公式,并给出了∂-方程的解.     

复流形上具有非光滑边界的强拟凸域上带权因子的Koppelman-Leray公式

利用权因子,我们得到了复流形上边界不必光滑的强拟凸域上（狆,狇）微分形式的带权因子的Ｋｏｐｐｅｌｍａｎ Ｌｅｒａｙ公式及其 方程的带权因子的解,其特点是不含有边界积分,从而避免了边界积分的复杂估计．其次,引进了权因子,带权因子的积分公式在应用上具有更大的灵活性．     

Stein流形局部q-凸域上不含边界积分的带权因子的同伦公式

利用权因子,得到了Steln流形局部q-凸域上不含边界积分的(r,s)型微分形式的带权因子的同伦公式及其     

Stein流形局部q—凸域上带权因子的同伦公式和e↓—方程

本文得到了Ｓｔｅｉｎ流形局部ｑ－凸域上（ｒ,Ｓ）型微分形式的带权因子的同伦公式及其ｅ－方程的带权因子的解。