紧致正则q伪凹CR流形族的整体$\bar\partial_{\bold M}$ -同伦及其$C^k$估计
Global $\bar\partial_{\bold M}$-homotopy with $C^k$ estimates for a family of compact, regular q-pseudoconcave CR manifolds
摘要：
设${\bold M}_0$是复流形${\bold G}$的紧致正则q-伪凹紧致CR子流形，${\cal B}$是${\bold G}$上的全纯向量丛，使得对于某个固定的$r<q$，有$\dim H^r({\bold M}_0, {\cal B}\big|_{\bold M})=0$.证明了$r$ -上同调的整体同伦公式及其$C^k$估计，其中${\cal B}$-上同调是任意CR子流形${\bold M}$上足够接近${\bold M}_0$的.
英文摘要：
Let ${\bold M}_0$ be a compact, regular q-pseudoconcave compact CR submanifold of a complex manifold ${\bold G}$ and ${\cal B}$ - a holomorphic vector bundle on ${\bold G}$ such that $\dim H^r({\bold M}_0, {\cal B}\big|_{\bold M})=0$ for some fixed $r<q$. We prove a global homotopy formula with $C^k$ estimates for $r$-cohomology of ${\cal B}$ on arbitrary CR submanifold ${\bold M}$ close enough to ${\bold M}_0$.
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