次椭圆Spin_C Dirac算子，I
Subelliptic Spin_C Dirac operators, I
摘要：
我们考虑修改的经典dbar-Neumann条件，定义Fredholm问题的Spin_C狄拉克算子。在第二部分中，我们使用边界层方法得到这些边值问题的次椭圆估计。利用这些结果，我们得到了严格伪凸流形的全纯欧拉示性数的有限部分作为具有次椭圆边界条件的Spin_C-Dirac算子的指数的表达式.我们还证明了一个类似的Agranovich Dynin公式表示在边界上的相对指数的指数的变化。若X是一个被严格伪凸超曲面剖分的复流形，则我们得到X的全纯欧拉示性数的公式，作为Spin_C-Dirac算子在其分支上的指数之和.这是一个次椭圆模拟Bojarski公式在椭圆的情况下。
英文摘要：
We consider modifications of the classical dbar-Neumann conditions that define Fredholm problems for the Spin_C Dirac operator. In part II, we use boundary layer methods to obtain subelliptic estimates for these boundary value problems. Using these results, we obtain an expression for the finite part of the holomorphic Euler characteristic of a strictly pseudoconvex manifold as the index of a Spin_C-Dirac operator with a subelliptic boundary condition. We also prove an analogue of the Agranovich-Dynin formula expressing the change in the index in terms of a relative index on the boundary. If X is a complex manifold partitioned by a strictly pseudoconvex hypersurface, then we obtain formulae for the holomorphic Euler characteristic of X as sums of indices of Spin_C-Dirac operators on the components. This is a subelliptic analogue of Bojarski's formula in the elliptic case.
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