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A Volume‐Area Inequality
Author(s) -
Miniowitz Ruth
Publication year - 1982
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/jlms/s2-25.1.88
Subject(s) - inequality , mathematics , volume (thermodynamics) , distortion (music) , boundary (topology) , set (abstract data type) , mathematical analysis , pure mathematics , computer science , physics , amplifier , bandwidth (computing) , programming language , computer network , quantum mechanics
We prove a Volume‐Area Inequality for quasiregular mappings which extends the familiar Ahlfors Cartwright Length‐Area Inequality for analytic functions. Using the Volume‐Area Inequality, we derive a distortion theorem, and some boundary behaviour for a special case, when the mappings are mean p ‐valent in volume with an empty branch set.