U.S.-Brazil Cooperative Research: Partial Differential Equations & Several Complex Variables

该奖项支持罗格斯大学的Francois Treves博士和巴西圣保罗大学的P.D.Cordaro博士在偏微分方程式和复变量方面的合作研究。本文将研究复向量场的交换系统(在光滑实流形上)的微分复形的局部解的存在性。最近，Cordaro和Treves得到了一般的必要条件，至少当特征集的秩为时是这样。1.Cordaro&Amp；Treves目前正在调查证明充分条件的可能性，特别是在柯西-黎曼结构的重要情况下。在顶级形式的情况下，有一个自然的猜想等待证明：如果Levi形式在任何点都不是确定的(正的或负的)，则局部可解性应该成立。这种类型的结果是通过Treves和他的合作者的努力，在过去十年中一直在建立的亚解析结构理论的完成的重要部分。该奖项将允许Cordaro&Amp；Treves定期聚在一起，为这个项目工作。Cordaro从CNPq NSF在巴西的相应机构获得了访问罗格斯大学的资金。特里维斯和一名研究生将回访圣保罗。

This award supports cooperative research on partial differ- ential equations and complex variables between Dr. Francois Treves of Rutgers University and Dr. P. D. Cordaro of the University of Sao Paulo, Sao Paulo, Brazil. The work will investigate the existence of local solutions in the differ- ential complexes originating from commuting systems of complex vector fields (on a smooth real manifold). Recently Cordaro and Treves have obtained general necessary conditions, at least when the rank of the characteristic set is . 1. Cordaro & Treves are currently investigating the possibility of proving sufficient conditions, in particular in the important case of Cauchy-Riemann structures. There is a natural conjecture that awaits proof, in the case of top-degree forms: local solvability ought to hold if the Levi form is not definite (positive or negative) at any point. This type of result is an essential part of the completion of the theory of hypo-analytic structures that has been building for the last ten years, through the efforts of Treves and his collaborators. The award will allow Cordaro & Treves to get together at regular intervals to work on this project. Cordaro has funds from CNPq NSF's corresponding agency in Brazil to visit Rutgers University. Treves and a graduate student will visit Sao Paulo in return.