ENGLISH

Some Novel Types of Fractal Geometry

By Stephen Semmes

Book information

Publisher
Oxford University Press
Year
2001
ISBN
1383021805, 0198508069, 9781383021806, 9780198508069
DOI
10.1093/oso/9780198508069.001.0001
LCC
QA614.86 .S46 2001
Open Library ID
OL7400127M
Language
english
Format
PDF
Filesize
8 MB (7995929 bytes)
Series
Oxford Mathematical Monographs
Edition
1
Pages
176\176
Library
Internet Archive
Orientation
portrait
Paginated
yes
Scanned
yes
Time added
2024-10-28 11:27:18

Description

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.

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