On Boundary Regularity of Analytic Discs

摘要

In this paper we study the boundary behavior of analytic discs near the zero set of a nonnegative plurisubharmonic function or a totally real submanifold of Cn . Our main result is the following. THzoasv 1.l. Let Ω be a complex manifold, p a plurisubharmonicfunction in Ω, and f:Δ→ Ω a holomorphic map of the unit disc Δ is contained in C into Ω such that p o f ≥ 0 and p o f(ξ) → 0 as ζis not an element of Δ trends to an open arc r is contained in δΔ . Assume that, for a certain point a is not an element of r, the cluster set C(f, a) contains a point p is not an elemnent of Ω such that p is strictly plurisubharmonic in a neighborkood ofp. Then f extende to a H0lder l/2-continuous mapping in a neighborkood of a on Δ U r. If, more- over, p > = 0 and thep function p` is plurisubharmonic in a neighborkood of p for some θ is no element of [1/2, l], then f is Hijlder l/2θ-continuous (Lipschitz, if 0 = l/2) in a neighborkood of　a on ΔUγ.