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Many parts of the subject of the boundary behavior of conformal mappings can be subsumed under the general heading of asymptotic representations of the Riemann mapping function near a boundary point. Asymptotic representations have, up to now, required that the boundary of the domain satisfy various types of regularity conditions. The results announced here give a method for obtaining asymptotic representations when the domain fails to satisfy such regularity conditions.

Asymptotic representation of conformal maps of strip domains without boundary regularity