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Description - Some Novel Types of Fractal Geometry by Stephen Semmes

The present book deals with fractal geometries which have features similar to ones of ordinary Euclidean spaces, while at the same time being quite different from Euclidean spaces in other ways. A basic type of feature being considered is the presence of Sobolev or Poincare inequalities, concerning the relationship between the average behaviour of a function and the average behaviour of its small-scale oscillations. Remarkable results in the last few years of Bourdon-Pajot and Laakso have shown that there is much more in the way of geometries like this than has been realized. Examples related to nilpotent Lie groups and Carnot metrics were known previously. On the other hand, 'typical' fractals that might be seen in pictures do not have these same kinds of features. 'Some Novel Types of Fractal Geometry' will be of interest to graduate students and researchers in mathematics, working in various aspects of geometry and analysis.

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Book Details

ISBN: 9780198508069
ISBN-10: 0198508069
Format: Hardback
(241mm x 161mm x 15mm)
Pages: 174
Imprint: Oxford University Press
Publisher: Oxford University Press
Publish Date: 28-Dec-2000
Country of Publication: United Kingdom

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Author Biography - Stephen Semmes

Professor Stephen Semmes, Mathematics Department, Rice University, Houston.