EQUATION ON COMPLEX MANIFOLDS

本文得到了复流形上边界不一定光滑的强拟凸域上的kOPPElMAn-lErAy公式，并得到这个域上的-方程的解的积分表示，这个表示的特点是不含边界的积分The author obtains the Koppelman Leray Formula For a strictly pseudoconvex domain with not necessarily smooth boundary in complex maniFolds, and an integral representation For the solution of equation on this domain is obtained

C~n中(p,q)型微分形式的-闭开拓

文中研究对给定在C~n中一域的边界上的C~(2)类(p,q)型微分形式越过边界的?闭开拓问题,得到了可以?闭开拓的二个充分必要条件和 Hartogs 与Bochner 型定理

BOCHNER TECHNIQUE ON STRONG KHLER-FINSLER MANIFOLDS

By using the Chern-Finsler connection and complex Finsler metric,the Bochner technique on strong Khler-Finsler manifolds is studied.For a strong Khler-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 obtaine

复流形q-凹域上不含边界积分的K-L-N公式

得到了复流形局部Q-凹域上(r,S)型微分形式的不含边界积分的kOPPElMAn-lErAy-nOrguET公式,这个公式特别适用于边界非光滑的局部Q-凹域,应用时不但可以避免繁复的估计,而且积分密度也不必在边界有定义.国家自然科学基金(批准号:19471066

Stein流形q-凸域上的同伦公式和-方程

得到了STEIn流形局部Q-凸域上(r,S)型微分形式的同伦公式和局部Q-凸域上(r,S)型(？)-方程的解,C--n空间的结果是它的特例。这个同伦公式在局部Q-凸域上(？)-方程的一致估计和Cr-流形的全纯开拓上有重要应用。国家自然科学基金资助项

Homotopy Formulas Without Boundary Integral and - Equation on Local q Convex Domains in Complex ManiFolds

得到复流形Q-凸域上（r，S）型微分形式的不含边界积分的同伦公式和局部Q-凸域上（r，S）型--方程的解，这个公式特别适用于边界非光滑的局部Q-凸域，这时不但可以避免繁复的估计，而且积分密度也不必在边界有定义.The homotopy Formulas without boundary integral of (r,s) diFFerential Forms and the solution of - equation of type (r,s) on local q convex domains in complex maniFolds are obtained.These Formulas are especially suitable For the case when the local q comvex domains with non smooth boundary, one can avoid complex esimates and the density of integral may be not deFined on the boundary but only in the domain.国家自然科学基

Koppelman Leray Norguet Formula for a Local q Concave Wedge in Complex Manifolds

得到复流形局部Q-凹域上（r，S）型微分形式的kOPPElMAn-lErAy-nOrguET公式，STEIn流形和Cn空间的结果是它的特例.The Koppelman Leray Norguet formala of (r,s) differential forms for a local q concave wedge in complex manifolds is obtained.国家自然科学基

Koppelman Formula on a SubmaniFold of Stein ManiFolds and Interpolation

本文得到了STEIn流形的子流形上的一个具有权因子的kOPPElMAn公式及一个内插公式。The koppelman Formula with weight Factors on a submaniFold of stein maniFolds isobtained,and an interpolation Formula is deduced.国家自然科学基

LEWY EQUATION ON STEIN MANIFOLDS

本文利用STEIn流形上强拟凸域的全纯支撑函数,并使用HErMITE度量和陈联络定义的kOPPElMAn-lErAy核,结合边界的流形结构特点,得到了强拟凸域边界上(P,Q)型lEWy方程(b-方程)解的一种整体积分表示.Using holomorphic support Function ofstrictly pseudoconvex domain on Stein maniFolds and the Koppelman-Leray kernel deFined by Hermitian metric and Chern connection, and Furthermore setting up a close connection with the characteristic property of the boundary, the author obtains a global integral representation of the solution of (p, q)-Form b-equation on the boundary of a strictly pseudoconvex domain.国家自然科学基

复流形上的Koppelan－Leray－Norguet公式及其应用

本文得到了复流形上具有逐块光滑边界的有界城d上的（P，Q）型微分形式的kOPPElMAn-lErAy-nOrguET公式，在适当假定下得到了d上方程的连续解.作为应用，得到了STEIn流形上实非退化强拟凸多面体上（P，Q）型微分形式的积分表示式以及实非退化强拟凸多面体上方程的连续解.国家自然科学基