On Some Problems in Several Complex Variables and Cr Geometry

0. Introduction. Geometric analysis in several complex variables and Cauchy Riemann geometry has been a quite active subject in pure and applied mathematics for decades. The classical work of Poincaré, Hartogs, Levi, E. Cartan, etc at the beginning of the century laid down part of the frame work of such a study. Since then, more and more attention has be paid to this field, as people discover its deep relationship with many fundamental problems in classical analysis and geometry, and its importance for partial differential equations, algebraic and symplectic geometry, topology, mathematical physics. In this note, we would like to present some results and problems along the lines of this research. Limited to the page numbers, we will focus our discussion on some of the problems, which the author’s recent work has touched upon. We will also have to leave out many important references, which can be found, say, in the survey paper of Forstneric [Fr1], the author’s papers [Hu1] [Hu2] [Hu3] [Hu6], and the recent reserach monographs of Baouendi-EbenfeltRothschild [BER2], D’Angelo [DA1] and Abate [Ab].