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 man...

We consider the space, CR(M), consisting of CR functions which also lie in L(M) on a quadric submanifold M of C of codimension at least one. For 1 ≤ p ≤ ∞, we prove that each element in CR(M) extends uniquely to an H function on the interior of the convex hull of M . As part of the proof, we establish a semi-global version of the CR approximation theorem of Baouendi and Treves for submanifolds ...

We define a class of generic CR submanifolds of C n of real codi-mension d, 1 ≤ d ≤ n − 1, called the Bloom-Graham model graphs, whose graphing functions are partially decoupled in their dependence on the variables in the real directions. We prove a global version of the Baouendi-Treves CR approximation theorem, for Bloom-Graham model graphs with a polynomial growth assumption on their graphing...

In this article we obtain the pinching of the null sectional curvature of CRlightlike submanifolds of an inde…nite Hermitian manifold. As a result of this inequality we conclude some non-existence results of such lightlike submanifolds.Moreover using the Index form we prove more non-existence results for CR-lightlike submanifolds. 1. Introduction The theory of submanifolds of a Riemannian or se...