Real Submanifolds in Complex Space and Their Mappings (PMS-47)

Presenting the main developments of the past two decades in the study of real submanifolds in complex space, this book covers the techniques in this area which borrow from real and complex analysis and partial differential equations, as well as from differential, algebraic and analytical geometry. One of the more important topics covered here is the holomorphic extension of functions and mappings that satisfy the tangential Cauchy-Riemann equations on rweal submanifolds, presenting the main results in this area. It also devotes attention to the study of holomorphic mappings between real submanifolds, and proves finite determination of such mappings by their jets under some optimal assumptions. Throughout the book, Cauchy-Riemann vector fields and their orbits play a central role.