Abstract: Let A_m^d={x₁,…,x_d)∈R^d:x₁>0,…,x_m>0,1 ≤ m ≤ d} be the angular domain in R^d(d≥2). In this paper we obtain the Martin's representation of positive harmonic functions in A_m^d,the relationship between the minimal harmonic functions and a zero-one law for conditioned Brownian motion are investigated, the representaive forms of the minimal harmonic functions in A_m^d are also presented.

Key words: Harmonic functions, Martin's representation, minimal harmonic functions, condi-tioned Brownian motion