Abstract
In this paper we will give an analytic proof of the following finiteness theorem for holomorphic families of Riemann surfaces: FIniteness Theorem OF Families. Let B be a Riemann surface of finite type. Then, there are only finitely many non-isomorphic and locally non-trivial holomorphic families of Riemann surfaces of fixed finite type (g, n) with 2g — 2 + n > 0 over B. KeywordsRiemann SurfaceHolomorphic MappingQuasiconformal MappingFinite TypeKleinian GroupThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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