Regularity of the boundaries of analytic sets

E. M. Chirka

Sbornik. Mathematics, Tome 45 (1983) no. 3, pp. 291-335

Résumé

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 $\mathbf C^n$ 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.