Classification theory is the investigation of families of Riemann surfaces which share some important property. As such, the subject has no bounds. In this chapter we shall confine ourselves to those results of classification theory on which the theory of principal functions has a direct bearing. In §1 we introduce the fundamental classes and prove the inclusion relations among them. In §2 we treat other properties and characterizations of these classes.
KeywordsHarmonic Function Riemann Surface Planar Surface Classification Theory Harmonic Measure
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