7 Subelliptic Spin C Dirac operators , II Basic Estimates
نویسندگان
چکیده
We assume that the manifold with boundary, X, has a SpinCstructure 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 Kähler. In this case the SpinCDirac 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 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.
منابع مشابه
Subelliptic Spin C Dirac operators, I
Let X be a compact Kähler manifold with strictly pseudoconvex boundary, Y. In this setting, the SpinC Dirac operator is canonically identified with ∂̄ + ∂̄∗ : C∞(X ; Λ) → C∞(X ; Λ). We consider modifications of the classical ∂̄-Neumann conditions that define Fredholm problems for the SpinC Dirac operator. In part 2, [7], we use boundary layer methods to obtain subelliptic estimates for these bound...
متن کاملar X iv : 0 70 5 . 16 99 v 2 [ m at h . A P ] 1 4 M ay 2 00 7 Subelliptic Spin C Dirac operators , II Basic Estimates
We assume that the manifold with boundary, X, has a SpinCstructure 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 Kähler. In this case the SpinCDirac operator ð agrees with ∂̄ + ∂̄∗ along the boundary. The induced CR-structure on bX is integrable and either strictly pseudoconvex...
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