Behavior Spaces on Finite Bordered Riemann Surfaces

2009-04-07T06:42:26Z

2009-04-07T06:42:26Z

1981-03

We introduced, in our previous work, behavior spaces for the purpose of a formulation of the Riemann-Roch theorem and Abel's theorem on open Riemann surfaces. The existence of behavior spaces on arbitrary Riemann surfaces was shown by using Zorn's Lemma. But behavior spaces are not very clear. So as to throw light on it, we shall give concretely some behavior spaces on finite bordered Riemann surfaces. If we use the specific kind of behavior space, our formulation of the theories is regarded as an obedient generalization of classical theories on compact surfaces. We shall give an example and show that meromorphic functions which is stated in our Riemann-Roch theorem are not always trivial on a surface with infinite genus and a large boundary. We shall give meromorphic functions on finite bordered Riemann surfaces whose real and imaginary parts have a certain behavior. This was unexpected on Riemann surfaces with large boundaries.

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Reprinted from the Memoirs of the Faculty of Industrial Arts, Kyoto Technical University, Science and Technology, Vol.29 (1980) pp.9-23

http://hdl.handle.net/10212/1903

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