Some novel types of fractal geometry
著者
書誌事項
Some novel types of fractal geometry
（Oxford mathematical monographs）
Oxford University Press , Clarendon Press, 2001
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注記
Includes bibliographical references (p. [154]-162) and index
内容説明・目次
内容説明
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.
目次
- 1. Introduction
- 2. Some background material
- 3. A few basic topics
- 4. Deformations
- 5. Mappings between spaces
- 6. Some more general topics
- 7. A class of constructions to consider
- 8. Geometric structures and some topological configurations
- Appendix A. A few side comments
- References
- Index
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