Conformal Dimension: Theory and Application

John M. Mackay, Jeremy T. Tyson

Research output: Book/Report/Conference proceedingBook


Conformal dimension measures the extent to which the Hausdorff dimension of a metric space can be lowered by quasisymmetric deformations. Introduced by Pansu in 1989, this concept has proved extremely fruitful in a diverse range of areas, including geometric function theory, conformal dynamics, and geometric group theory.

This survey leads the reader from the definitions and basic theory through to active research applications in geometric function theory, Gromov hyperbolic geometry, and the dynamics of rational maps, amongst other areas. It reviews the theory of dimension in metric spaces and of deformations of metric spaces. It summarizes the basic tools for estimating conformal dimension and illustrates their application to concrete problems of independent interest. Numerous examples and proofs are provided.
Original languageEnglish (US)
PublisherAmerican Mathematical Society
ISBN (Print)9780821852293
StatePublished - 2010

Publication series

NameUniversity Lecture Series


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