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Riemann Surfaces

Simon Donaldson


The theory of Riemann surfaces occupies a very special place in mathematics. It is a culmination of much of traditional calculus, making surprising connections with geometry and arithmetic. It is an extremely useful part of mathematics, knowledge of which is needed by specialists in many other fields. It provides a model for a large number of more recent developments in areas including manifold topology, global analysis, algebraic geometry, Riemannian geometry, and diverse topics in mathematical physics. This text on Riemann surface theory proves the fundamental analytical results on the exist ... More

Keywords: Riemann surfaces, traditional calculus, manifold topology, global analysis, algebraic geometry, Riemannian geometry, mathematical physics, Riemann surface theory, meromorphic functions, Uniformisation Theorem

Bibliographic Information

Print publication date: 2011 Print ISBN-13: 9780198526391
Published to Oxford Scholarship Online: December 2013 DOI:10.1093/acprof:oso/9780198526391.001.0001


Affiliations are at time of print publication.

Simon Donaldson, author
Royal Society Research Professor, Imperial College, London