Uniformization of Riemann Surfaces
Revisiting a hundred-year-old theorem
Henri Paul de Saint-Gervais
Paris
A subscription is required to access this book.
| FrontmatterDownload pp. i–iv | |
| ContentsDownload pp. v–vi | |
| The AuthorsDownload p. vii | |
| ForewordDownload pp. ix–xi | |
| General introduction: The uniformization theoremDownload pp. xiii–xxx | |
| Part A Riemann surfacesp. 1 | |
| I | Antecedent workspp. 3–24 |
| II | Riemannpp. 25–73 |
| III | Riemann surfaces and Riemannian surfacespp. 75–95 |
| IV | Schwarz’s contributionpp. 97–112 |
| Intermezzop. 113 | |
| V | The Klein quarticpp. 115–138 |
| Part B The method of continuityp. 139 | |
| Part B The method of continuityDownload pp. 141–147 | |
| VI | Fuchsian groupspp. 149–179 |
| VII | The “method of continuity”pp. 181–197 |
| VIII | Differential equations and uniformizationpp. 199–233 |
| IX | Examples and further developmentspp. 235–279 |
| Intermezzop. 281 | |
| X | Uniformization of surfaces and the equation pp. 283–319 |
| Part C Towards the general uniformization theoremp. 321 | |
| Part C Towards the general uniformization theoremDownload pp. 323–332 | |
| XI | Uniformization of functionspp. 333–352 |
| XII | Koebe’s proof of the uniformization theorempp. 353–360 |
| XIII | Poincaré’s proof of the uniformization theorempp. 361–376 |
| Epilogue | The uniformization theorem from 1907 to 2007pp. 377–381 |
| Appendicesp. 383 | |
| The correspondence between Klein and Poincarépp. 385–416 | |
| Some historical reference pointspp. 417–439 | |
| Bibliographypp. 441–469 | |
| Indexpp. 471–482 |