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Uniformization of Riemann Surfaces =...

de Saint-Gervais, Henri Paul,

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Uniformization of Riemann Surfaces = Revisiting a hundred-year-old theoremTranslated from the French by Robert G. Burns /

Record Type:	Electronic resources : Monograph/item
Title/Author:	Uniformization of Riemann Surfaces/ Henri Paul de Saint-Gervais
Reminder of title:	Revisiting a hundred-year-old theoremTranslated from the French by Robert G. Burns /
Author:	de Saint-Gervais, Henri Paul,
Published:	Zuerich, Switzerland :European Mathematical Society Publishing House, : 2016,
Description:	1 online resource (512 pages)
Subject:	History of mathematics -
Online resource:	https://doi.org/10.4171/145
Online resource:	https://www.ems-ph.org/img/books/gervais_mini.jpg
ISBN:	9783037196458

Uniformization of Riemann Surfaces = Revisiting a hundred-year-old theoremTranslated from the French by Robert G. Burns /
de Saint-Gervais, Henri Paul,

Uniformization of Riemann SurfacesRevisiting a hundred-year-old theoremTranslated from the French by Robert G. Burns /[electronic resource] :Henri Paul de Saint-Gervais - Zuerich, Switzerland :European Mathematical Society Publishing House,2016 - 1 online resource (512 pages) - Heritage of European Mathematics (HEM) ;2523-5214.

Restricted to subscribers:https://www.ems-ph.org/ebooks.php

In 1907 Paul Koebe and Henri Poincar é almost simultaneously proved the uniformization theorem: Every simply connected Riemann surface is isomorphic to the plane, the open unit disc, or the sphere. It took a whole century to get to the point of stating this theorem and providing a convincing proof of it, relying as it did on prior work of Gauss, Riemann, Schwarz, Klein, Poincar é, and Koebe, among others. The present book offers an overview of the maturation process of this theorem. The evolution of the uniformization theorem took place in parallel with the emergence of modern algebraic geometry, the creation of complex analysis, the fi\u000crst stirrings of functional analysis, and with the flowering of the theory of differential equations and the birth of topology. The uniformization theorem was thus one of the lightning rods of 19th century mathematics. Rather than describe the history of a single theorem, our aim is to return to the original proofs, to look at these through the eyes of modern mathematicians, to enquire as to their correctness, and to attempt to make them rigorous while respecting insofar as possible the state of mathematical knowledge at the time, or, if this should prove impossible, then using modern mathematical tools not available to their authors. This book will be useful to today's mathematicians wishing to cast a glance back at the history of their discipline. It should also provide graduate students with a non-standard approach to concepts of great importance for modern research.

ISBN: 9783037196458

Standard No.: 10.4171/145doiSubjects--Topical Terms:

3480938
History of mathematics

Uniformization of Riemann Surfaces = Revisiting a hundred-year-old theoremTranslated from the French by Robert G. Burns /
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