Infinitesimal Geometry of Quasiconformal and Bi-Lipschitz Mappings in the Plane
Bogdan Bojarski
IM PAN, Warsaw, PolandVladimir Gutlyanskii
National Academy of Science of Ukraine, Donetsk, UkraineOlli Martio
Finnish Academy of Science and Letters, Helsinki, FinlandVladimir Ryazanov
National Academy of Science of Ukraine, Donetsk, Ukraine
A subscription is required to access this book.
| FrontmatterDownload pp. i–iv | |
| PrefaceDownload p. v | |
| ContentsDownload pp. vii–ix | |
| Part I Quasiconformal Mappings in the Planep. 1 | |
| 1 | Background of the theorypp. 3–18 |
| 2 | Conformal invariantspp. 19–33 |
| 3 | Definitions of quasiconformal mapspp. 34–48 |
| 4 | Compactness and convergence theorypp. 49–57 |
| 5 | Beltrami differential equationpp. 58–83 |
| Part II Infinitesimal Geometry of Quasiconformal Mapsp. 85 | |
| 6 | Infinitesimal spacepp. 87–106 |
| 7 | Asymptotically conformal curvespp. 107–116 |
| 8 | Conformal differentiabilitypp. 117–130 |
| 9 | Points of maximal stretchingpp. 131–137 |
| 10 | Lipschitz continuity of quasiconformal mapspp. 138–149 |
| 11 | Regularity of quasiconformal curvespp. 150–156 |
| 12 | Regularity of conformal maps at the boundarypp. 157–160 |
| Part III Applications of Quasiconformal Mapsp. 161 | |
| 13 | John’s rotation problempp. 163–171 |
| 14 | Variation of quasiconformal mapspp. 172–179 |
| 15 | Criteria of univalencepp. 180–183 |
| Bibliographypp. 185–201 | |
| Indexpp. 203–205 |