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Some Novel Types of Fractal Geometry Stephen Semmes

Some Novel Types of Fractal Geometry

Stephen Semmes

Published December 28th 2000
ISBN : 9780198508069
Hardcover
164 pages
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 About the Book 

This text deals with fractal geometries which have features similar to ones of ordinary Euclidean spaces, while at the same time being different from Euclidean spaces in other ways. A basic type of feature being considered is the presence of SobolevMoreThis text deals with fractal geometries which have features similar to ones of ordinary Euclidean spaces, while at the same time being 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.