Some Novel Types of Fractal Geometry (Oxford Mathematical Monographs) (Hardcover)

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Description


This book deals with fractal geometries that have features similar to ones of ordinary Euclidean spaces, while at the same time being quite different from Euclidean spaces.. A basic example of this feature considered is the presence of Sobolev or Poincar inequalities, concerning the relationship between the average behavior of a function and the average behavior of its small-scale oscillations. Remarkable results in the last few years through Bourdon-Pajot and Laakso have shown that there is much more in the way of geometries like this than have been realized, only examples related to nilpotent Lie groups and Carnot metrics were known previously. On the other had, 'typical' fractals that might be seen in pictures do not have these same kinds of features. This text examines these topics in detail and will interest graduate students as well as researchers in mathematics and various aspects of geometry and analysis.


Product Details
ISBN: 9780198508069
ISBN-10: 0198508069
Publisher: Oxford University Press, USA
Publication Date: March 15th, 2001
Pages: 176
Language: English
Series: Oxford Mathematical Monographs