Subelliptic SpinC Dirac operators, II basic estimates
成果类型：
Article
署名作者：
Epstein, Charles L.
刊物名称：
ANNALS OF MATHEMATICS
ISSN/ISSBN：
0003-486X
DOI：
10.4007/annals.2007.166.723
发表日期：
2007
页码：
723-777
关键词：
摘要：
We assume that the manifold with boundary, X, has a Spin(C)-structure with spinor bundle $. 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 Spin(C)-Dirac operator a agrees with (partial derivative) over bar +(partial derivative) over bar* 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 Spin(C)-Dirac operator acting on sections on $ 0 E. We use boundary conditions that are modifications of the classical (partial derivative) over bar -Neumann condition. These results are proved by using the extended Heisenberg calculus.