Description of Some of my Recent Research Work

My recent research work has focused on numerous problems in Complex Analysis of Several Variables which are also related to questions in non-linear analysis, partial differential equations, differential geometry and classical dynamics. More specifically, I have been working on the following topics: (1). Normal form theory and holomorphic equivalence problem of real submanifolds in a complex manifold, holomorphic hulls of real submanifolds in complex spaces, the complex Plateau problem, as well as their interaction with celestial mechanics, KAM theory, etc; (2). Rigidity problems in several complex variables, as well as their applications and interactions with super-rigidity problems in the theory of complex singularities, complex geometry, and classical dynamics; (3). CR deformation of a compact strongly pseudoconvex CR manifold; simultaneous embedding of a CR family of strongly pseudoconvex CR manifolds; the fiber normality problem for a Stein filling of a (1,1) convex-concave family. (4). Chern-Moser-Weyl tensor and applications to the embedding and unique continuation problem for CR maps. My research on these problems has been continuously supported by the National Science Foundation, and my most two recent research grants (DMS-1101481, DMS-0801056) were funded by the NSF with the highest priority. The following paragraphs contain a more detailed discussion of some of my research activities with an emphasis mainly on work in the past six years: Papers cited below are posted in my home web page: www.math.rutgers.edu/∼huangx