This reference details valuable results that lead to improvements
in existence theorems for the Loewner differential equation in
higher dimensions, discusses the compactness of the analog of the
Caratheodory class in several variables, and studies various
classes of univalent mappings according to their geometrical
definitions. It introduces the infinite-dimensional theory and
provides numerous exercises in each chapter for further study. The
authors present such topics as linear invariance in the unit disc,
Bloch functions and the Bloch constant, and growth, covering and
distortion results for starlike and convex mappings in Cn and
complex Banach spaces.
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