Henri Poincaré and the Uniformization of Riemann Surfaces

Abstract

Uniformization of Riemann surfaces is one of the mathematical problems that have accompanied H. Poincaré all along his mathematical life. I shall evoke six “uniformization theorems” discovered by Poincaré. He proved the first of these six theorems when he was a twenty-six years old assistant professor in Caen, and the last one twenty-six years later, when he was one of the most celebrated scientists in the world.

The present text is in large part extracted from the book that Henri- Paul de Saint-Gervais has written about the history of the uniformization of Riemann surfaces ([St-Gervais2010]).