The structure of proper holomorphic mappings of a planar domain onto a simply connected domain
Abstract
It can be easily shown that all the proper one to one holomorphic functions from a bounded simply conncected domain onto the right half plane, such that a chosen point on the boundary gets mapped to infinity, are rational functions of the Riemann map on the domain and are also rational functions of the image of the boundary point under the Riemann map if the boundary point is allowed to vary. In this work, we have derived analogous results in case of a multiply connected planar domain and have shown that all the proper n to 1 holomorphic functions from an n-connected domain onto the right half plane, such that one point on each boundary component gets mapped to infinity, are rational functions of 2 Ahlfors maps and are also rational functions of the images of the chosen boundary points under the 2 Ahlfors maps if the boundary points are allowed to vary.
Degree
Ph.D.
Advisors
Bell, Purdue University.
Subject Area
Mathematics
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