论文标题
正式可集成的结构I.溶液束带的分辨率
Formally Integrable Structures I. Resolution of Solution Sheaves
论文作者
论文摘要
这是关于正式集成结构的$ l^2 $理论的一系列论文中的第一篇。它致力于为L. H {Ö} rmander引入的一类过度确定的系统构建解决方案的分解。获得了足够的全球精确度条件，这导致了表弟类型问题的局部解决方案的胶合技术。此外，我们还证明了TREVES复合物的局部溶解性，用于具有消失的Levi形式的正式集成结构，包括Levi平坦结构作为特殊情况。据作者所知，只不过是椭圆案例已经知道了Levi Flat Case中Treves Complex的本地$ l^2 $ - 可辨方差。
This is the first of a series of papers on the $L^2$-theory for formally integrable structures. It is devoted to constructing a resolution of the solution sheaf for a class of overdetermined systems introduced by L. H{ö}rmander. A sufficient condition for global exactness is obtained, which leads to gluing techniques for local solutions formulated as Cousin type problems. In addition, we also prove the local solvability of the Treves complex for formally integrable structures with vanishing Levi forms, including Levi flat structures as special cases. To the best of the authors' knowledge, nothing more than the elliptic case is known about the local $L^2$-solvability of the Treves complex in the Levi flat case.
