Journal of the Ramanujan Mathematical Society

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Proper Holomorphic Maps of Plane Domains of Finite Connectivity


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1 Department of Mathematics, S.I.W.S. College, 337, Sewree-Wadala Estate, Wadala, Mumbai 400 031, India
     

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In this note, we give a proof of the fact that if Ω and Ω' are domains of finite connectivity ≥ 3 in ℂ, then the number of proper holomorphic maps from Ω to Ω' is finite. As a special case we deduce a well known result that Aut(Ω) is finite for any domain Ω in ℂ of finite connectivity ≥ 3.
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  • Proper Holomorphic Maps of Plane Domains of Finite Connectivity

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Authors

Gollakota V. V. Hemasundar
Department of Mathematics, S.I.W.S. College, 337, Sewree-Wadala Estate, Wadala, Mumbai 400 031, India

Abstract


In this note, we give a proof of the fact that if Ω and Ω' are domains of finite connectivity ≥ 3 in ℂ, then the number of proper holomorphic maps from Ω to Ω' is finite. As a special case we deduce a well known result that Aut(Ω) is finite for any domain Ω in ℂ of finite connectivity ≥ 3.