Some novel types of fractal geometry /
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Oxford : New York :
Clarendon Press ; Oxford University Press,
2001
Oxford : New York : [2001], ©2001 Oxford : New York : c2001 |
| Series: | Oxford mathematical monographs
Oxford mathematical monographs Oxford mathematical monographs |
| Subjects: |
Table of Contents:
- Some background material
- A few basic topics
- Deformations
- Mapping between spaces
- Some more general topics
- A class of constructions to consider
- Geometric structures and some topological configurations
- Appendix. Some side comments
- 1 Introduction
- 1.1. Some aspects of "calculus" on Euclidean spaces
- 1.2. General metric spaces
- 1.3. The present monograph
- 1.4. Another perspective: curve families in metric spaces
- 2. Some background material
- 2.1. Doubling spaces
- 2.2. Ahlfors-regular spaces
- 2.3. Poincare inequalities
- 2.4. Comparisons and examples
- 2.5. BPI spaces and BPI equivalence
- 3. A few basic topics
- 3.1. Only countably many?
- 3.2. A universal argument
- 3.3. Rectifiability
- 3.4. A slightly dumb case: dimensions [less than or equal to] 1
- 4. Deformations
- 4.1. Some general notions and examples
- 4.2. Doubling measures
- 4.3. Returning to general themes
- 4.4. Another view of the previous sections
- 5. Mappings between spaces
- 5.1. Questions, conjectures, and former conjectures
- 5.2. Regular mappings
- 5.3. Weak tangents
- 5.4. Finding "regular" behavior in Lipschitz mappings
- 5.5. "Decent calculus" and regular mappings
- 6. Some more general topics
- 6.1. A class of spaces, as from Laakso
- 6.2. Extremality
- 6.3. Looking at sets inside of spaces with "decent calculus"
- 6.4. Minimality and compression
- 6.5. Embeddings
- 7. A class of constructions to consider
- 7.1. The Heisenberg groups
- 7.2. The Heisenberg fibrations
- 7.3. questions about finding "fibrations" with interesting structure
- 7.4. (s,t)-Regular mappings
- 7.5. Some properties of (s,t)-regular mappings
- 7.6. Special structure in particular situations
- 7.7. (s,t)-Regular mappings and pushing geometry forward
- 8. Geometric structures and some topological configurations.
- 1 Introduction. 1.1. Some aspects of "calculus" on Euclidean spaces. 1.2. General metric spaces. 1.3. The present monograph. 1.4. Another perspective: curve families in metric spaces
- 2. Some background material. 2.1. Doubling spaces. 2.2. Ahlfors-regular spaces. 2.3. Poincare inequalities. 2.4. Comparisons and examples. 2.5. BPI spaces and BPI equivalence
- 3. A few basic topics. 3.1. Only countably many? 3.2. A universal argument. 3.3. Rectifiability. 3.4. A slightly dumb case: dimensions [less than or equal to] 1
- 4. Deformations. 4.1. Some general notions and examples. 4.2. Doubling measures. 4.3. Returning to general themes. 4.4. Another view of the previous sections
- 5. Mappings between spaces. 5.1. Questions, conjectures, and former conjectures. 5.2. Regular mappings. 5.3. Weak tangents. 5.4. Finding "regular" behavior in Lipschitz mappings. 5.5. "Decent calculus" and regular mappings
- 6. Some more general topics. 6.1. A class of spaces, as from Laakso. 6.2. Extremality. 6.3. Looking at sets inside of spaces with "decent calculus" 6.4. Minimality and compression. 6.5. Embeddings
- 7. A class of constructions to consider. 7.1. The Heisenberg groups. 7.2. The Heisenberg fibrations. 7.3. questions about finding "fibrations" with interesting structure. 7.4. (s,t)-Regular mappings. 7.5. Some properties of (s,t)-regular mappings. 7.6. Special structure in particular situations. 7.7. (s,t)-Regular mappings and pushing geometry forward
- 8. Geometric structures and some topological configurations.