REGULARITY OF THE BOUNDARIES OF ANALYTIC SETS

Abstract

In this article the author studies the boundary behavior of a one-dimensional complex analytic set A in a neighborhood of a totally real manifold M in Cn with smoothness greater than 1. He proves that the limit points of A on M form a set of locally finite length and that near almost every limit point the closure of A is either a manifold with boundary (with smoothness corresponding to M) or a union of two manifolds with boundary. He investigates the structure of the tangent cone to A at the limit points and proves a theorem concerning the boundary regularity of holomorphic discs glued to M. Bibliography: 22 titles.