A New Construction of Riemann Surfaces with Corona
نویسندگان
چکیده
equivalently [Gar,VIII.2], the corona M(X) \ ι(X) is empty. (Here M(X) is the maximal ideal space of the algebra H∞(X) of bounded holomorphic functions on X and ι is the natural inclusion X ↪→ M(X).) If X does not satisfy the corona theorem then X may be said to have corona. Riemann surfaces known to satisfy the corona theorem include the unit disk [Car], bordered Riemann surfaces [All] [Sto], and various classes of planar domains [GaJo] [Moo]. The question of whether general planar domains satisfy the corona theorem is open. The first construction of a Riemann surface with corona is due to Cole [Gam]. The goal of this paper is to prove the following.
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