AUTOMORPHISM GROUPS ON CERTAIN REINHARDT DOMAINS

  • Published : 1993.08.01

Abstract

In this paper, we show that Greene-Krantz's conjecture is true for certain class of domains. In fact, we give a complete classification of automorphism groups of domains of the form (Fig.) where the function .phi. is a real valued $C^{\infty}$ function in a neighborhood of [0,1] which satisfies the following conditions; (1) .phi.(0)=.phi.'(0)=0 and .phi.(1)=1, (2) .phi.(t) is increasing and convex for t>0.vex for t>0.

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