Uniformization of Riemann Surfaces

Revisiting a hundred-year-old theorem

  • Henri Paul de Saint-Gervais

    Paris
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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
IAntecedent workspp. 3–24
IIRiemannpp. 25–73
IIIRiemann surfaces and Riemannian surfacespp. 75–95
IVSchwarz’s contributionpp. 97–112
Intermezzop. 113
VThe Klein quarticpp. 115–138
Part B The method of continuityp. 139
Part B The method of continuityDownload pp. 141–147
VIFuchsian groupspp. 149–179
VIIThe “method of continuity”pp. 181–197
VIIIDifferential equations and uniformizationpp. 199–233
IXExamples and further developmentspp. 235–279
Intermezzop. 281
XUniformization of surfaces and the equation Δgu=2euϕ\Delta_g u = 2 e^u - \phipp. 283–319
Part C Towards the general uniformization theoremp. 321
Part C Towards the general uniformization theoremDownload pp. 323–332
XIUniformization of functionspp. 333–352
XIIKoebe’s proof of the uniformization theorempp. 353–360
XIIIPoincaré’s proof of the uniformization theorempp. 361–376
EpilogueThe 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Some historical reference pointspp. 417–439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

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