Subelliptic Spin C Dirac operators, II Basic estimates
Subelliptic Spin C Dirac operators, II Basic estimates
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DOI：
10.4007/annals.2007.166.723
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发表时间：
2007-05
影响因子：
4.9
通讯作者：
C. Epstein
中科院分区：
文献类型：
--
作者：
C. Epstein
我们假设有边界的流形X具有具有旋量丛S的自旋C-结构。在边界上，该结构与无穷阶、可积、几乎复数结构所定义的结构一致，度量为Kahler。在这种情况下，自旋C-狄拉克算符沿边界与∂+∂∗一致。BX上的诱导CR-结构是可积的，且要么是严格伪凸的，要么是严格伪凹的。我们假设E→X是一个复向量丛，它沿BX具有无穷阶、可积的复结构，且与沿BX定义的复结构相容。本文用边界层方法证明了作用于S/⊗E上的截面上的扭转C-狄拉克算子的亚椭圆估计。我们使用的边界条件是经典的∂-Neumann条件的修正。用推广的海森堡微积分证明了这些结果。
We assume that the manifold with boundary, X, has a SpinC-structure with spinor bundle S /. Along the boundary, this structure agrees with the structure defined by an infinite order, integrable, almost complex structure and the metric is Kahler. In this case the SpinC-Dirac operator ð agrees with ¯ ∂ + ¯ ∂ ∗ along the boundary. The induced CR-structure on bX is integrable and either strictly pseudoconvex or strictly pseudoconcave. We assume that E → X is a complex vector bundle, which has an infinite order, integrable, complex structure along bX, compatible with that defined along bX. In this paper we use boundary layer methods to prove subelliptic estimates for the twisted SpinC-Dirac operator acting on sections on S / ⊗ E. We use boundary conditions that are modifications of the classical ¯ ∂-Neumann condition. These results are proved by using the extended Heisenberg calculus.