The theory of Riemann surfaces has a geometric and an analytic part. The
former deals with the axiomatic definition of a Riemann surface, methods
of construction, topological equivalence, and conformal mappings of one
Riemann surface on another. The analytic part is concerned with the
existence and properties of functions that have a special character
connected with the conformal structure, for instance: subharmonic,
harmonic, and analytic functions.
Originally published in 1960.
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