Some Novel Types of Fractal Geometry
By (author) Stephen Semmes
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Some Novel Types of Fractal Geometry by Stephen Semmes
Book DescriptionThe 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 DetailsISBN: 9780198508069
(241mm x 161mm x 15mm)
Imprint: Oxford University Press
Publisher: Oxford University Press
Publish Date: 28-Dec-2000
Country of Publication: United Kingdom
Books By Author Stephen Semmes
Graphic Apology for Symmetry and Implicitness, Hardback (June 2000)
Succinct representation and fast access to large amounts of data are challenges of our time. This unique book suggests general approaches of 'complexity of descriptions'. It deals with a variety of concrete topics and bridges between them, while opening new perspectives and providing promising avenues for the 'complexity puzzle'.
Fractured Fractals and Broken Dreams, Hardback (November 1997)» View all books by Stephen Semmes
Fractal geometrics can arise in many different ways mathematically. This book proposes notions of coherent geometric structure, asking what exactly is a fractal "pattern"? A wide range of problems are dealt with, and examples given, which connect to other diverse areas of mathmatics.
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Author Biography - Stephen Semmes
Professor Stephen Semmes, Mathematics Department, Rice University, Houston.
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