Lectures on Analysis on Metric Spaces
Analysis in spaces with no a priori smooth structure has progressed to include concepts from the first order calculus. In particular, there have been important advances in understanding the infinitesimal versus global behavior of Lipschitz functions and quasiconformal mappings in rather general sett...
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| Format: | eBook |
| Language: | English |
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New York, NY
Springer New York
2001, 2001
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| Edition: | 1st ed. 2001 |
| Series: | Universitext
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| Subjects: | |
| Online Access: | |
| Collection: | Springer Book Archives -2004 - Collection details see MPG.ReNa |
Table of Contents:
- 1. Covering Theorems
- 2. Maximal Functions
- 3. Sobolev Spaces
- 4. Poincaré Inequality
- 5. Sobolev Spaces on Metric Spaces
- 6. Lipschitz Functions
- 7. Modulus of a Curve Family, Capacity, and Upper Gradients
- 8. Loewner Spaces
- 9. Loewner Spaces and Poincaré Inequalities
- 10. Quasisymmetric Maps: Basic Theory I
- 11. Quasisymmetric Maps: Basic Theory II
- 12. Quasisymmetric Embeddings of Metric Spaces in Euclidean Space
- 13. Existence of Doubling Measures
- 14. Doubling Measures and Quasisymmetric Maps
- 15. Conformal Gauges
- References