000			02103 a2200217 4500
003			OSt
040			_cIIT Kanpur
041			_aeng
082			_a515.93 _bD714r
100			_aDonaldson, Simon
245			_aRiemann surfaces _cSimon Donaldson
260			_bOxford University Press _c2011 _aOxford
300			_axiv, 286p
440			_aOxford graduate texts in mathematics series
490			_vv.22
520			_aThe 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, anddiverse topics in mathematical physics.This graduate text on Riemann surface theory proves the fundamental analytical results on the existence of meromorphic functions and the Uniformisation Theorem. The approach taken emphasises PDE methods, applicable more generally in global analysis. The connection with geometric topology, and in particular the role of the mapping class group, is also explained. To this end, some more sophisticated topics have been included, compared with traditional texts at this level. While the treatment isnovel, the roots of the subject in traditional calculus and complex analysis are kept well in mind.Part I sets up the interplay between complex analysis and topology, with the latter treated informally. Part II works as a rapid first course in Riemann surface theory, including elliptic curves. The core of the book is contained in Part III, where the fundamental analytical results are proved. Following this section, the remainder of the text illustrates various facets of the more advanced theory.
650			_aRiemann surfaces
650			_aFunctions
856			_uhttps://ebookcentral.proquest.com/lib/iitk-ebooks/detail.action?docID=3055739&query=3055739
942			_cEBK
999			_c565957 _d565957