A weak pseudoconcavity condition for abstract almost CR manifolds
A weak pseudoconcavity condition for abstract almost CR manifolds
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DOI：
10.1007/s002220000089
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发表时间：
2000-11
影响因子：
3.1
通讯作者：
C. Hill;M. Nacinovich
中科院分区：
文献类型：
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作者：
C. Hill;M. Nacinovich
在抽象CR流形M的背景下，证明了作用在(p，0)-形式上的∂M-算子的一个次椭圆估计.在p=0的情况下，我们允许几乎CR流形.它意味着相关偏微分方程解的L2解的光滑性，以及CR函数的弱最大模原理和强最大模原理的有效性，后者在证明了弱唯一连续定理后推广了[DCN]中的结果。我们所考虑的相关偏微分方程组非常适合研究复杂的CR向量丛。特别地，对于紧M，我们得到了关于整体截面空间的有限维的结果，以及关于它们的第一上同调群的Hausdorff性的结果。这些结果是在本质伪凹性的假设下得到的，本质伪凹性应该被认为是伪凹性的弱版本，
In this paper we prove a subelliptic estimate for the∂ M–operator acting on (p, 0)-forms, in the context of an abstract CR manifold M. In the case p= 0 we allow almost CR manifolds. It implies smoothness of L2 loc–solutions of related partial differential equations; and also the validity of the weak and strong maximum modulus principles for CR functions, the latter after proving a weak unique continuation theorem generalizing that in [DCN]. The related partial differential equations we consider are quite well suited to the investigation of complex CR vector bundles. In particular we obtain, for compact M, results about the finite dimensionality of the space of global sections, and on the Hausdorffness of their first cohomology groups. These results are obtained under an assumption of essential pseudoconcavity, which should be thought as a weak version of pseudoconcavity,