Some Novel Types of Fractal Geometry

Stephen Semmes

ISBN 10: 0198508069 / ISBN 13: 9780198508069

Published by Oxford University Press, GB, 2000

About this Item

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 Poincaré 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.

Seller Inventory # LU-9780198508069

Bibliographic Details

• Title: Some Novel Types of Fractal Geometry
• Publisher: Oxford University Press, GB
• Publication Date: 2000
• Language: English
• ISBN 10: 0198508069
• ISBN 13: 9780198508069
• Binding: Hardback
• Condition: New
• Dimensions: 23.39W x 1.12H x 15.6D centimeters 23.39 centimeters width by 1.12 centimeters height by 15.6 centimeters depth
• Weight: 392 grams

About this title

Synopsis

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 Poincaré 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.

About the Author

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