This book documents the rich structure of the holomorphic Q functions which are geometric in the sense that they transform naturally under conformal mappings. Particular emphasis is placed on recent developments based on the interaction between geometric function / measure theory and other branches of mathematical analysis, including potential theory, complex variables, harmonic analysis, functional analysis, and operator theory. Largely self-contained, this book will be an instructional and reference work for advanced courses and research in conformal analysis, geometry, and function spaces.

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