On Bounded Positive(m,p)-Circle Domains

Let D be a bounded positive(m, p)-circle domain in C~2. The authors prove that if dim(Iso(D)~0) = 2, then D is holomorphically equivalent to a Reinhardt domain; if dim(Iso(D)~0) = 4, then D is holomorphically equivalent to the unit ball in C~2. Moreover,the authors prove the Thullen's classification on bounded Reinhardt domains in C~2 by the Lie group technique.