Project information
Local geometric properties of weakly pseudoconvex manifolds

This project is based on the author´s dissertation (Princeton 1995) and his subsequent results. In the PhD-thesis, supervised by prof. J.J. Kohn, the founder of this project, the author obtained results which open new possibilities in the study of local geometry of pseudoconvex surfaces of finite type. Previously, the study of such surfaces was generally restricted to qualitative analysis, without precise quantitative results. The disertation gives completely explicit sufficient (and in the case of the so called Kohn-Nirenberg domains) exact condition for the existence of basic geometric objects, and use the techniques for the study of other geometric objects on CR manifolds. More specifically, this means finding necessary conditions in the general cas e, answering remaining open questions in type four, finding a complete set of local biholomorphic invariants and the study of complex geodesics.