Holomorphic extension and approximation of Cauchy-Riemann functions

The Cauchy-Riemann theory is a new branch of complex analysis dealing with geometry of smooth real submanifolds of complex manifolds, together with the structure induced on the submanifolds by the complex structure of the ambient manifolds, and with the properties of functions on the submanifolds which satisfy some system of partial differential equations induced by complex structures. Some problems of the Cauchy-Riemann theory are discussed here. 18 refs