Uniformization of Riemann Surfaces

BookshemMonograph

Revisiting a hundred-year-old theorem

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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
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 $Δ_{g} u = 2 e^{u} - ϕ$ 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	Some historical reference pointspp. 417–439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