SOME NOVEL TYPES OF FRACTAL GEOMETRY by Stephen Semmes ( 9780198508069 )

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Title:

SOME NOVEL TYPES OF FRACTAL GEOMETRY

By:

Stephen Semmes

Format:

Hardback

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£167.50

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£146.56

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ISBN 10:

0198508069

ISBN 13:

9780198508069

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Publisher:

OXFORD UNIVERSITY PRESS

Pub. date:

28 December, 2000

Series:

Oxford Mathematical Monographs

Pages:

174

Description:

Fractals are curves or surfaces generated by some repeated process involving successive subdivision, and notions concerning fractal geometry and examples of fractal behaviour are well-known. The present book deals with certain types of fractal geometry which are rather different from typical ones. Recent works have shown that these kinds of fractal spaces are more plentiful than one might have expected. This book will be of interest to graduate students, lecturers,and researchers working in various aspects of geometry and analysis.

Synopsis:

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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Imprint:

Oxford University Press

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Returnable

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