Although Riemann surfaces are a time-honoured field, this book is novel in its broad perspective that systematically explores the connection with other fields of mathematics. It can serve as an introduction to contemporary mathematics as a whole as it develops background material from algebraic topology, differential geometry, the calculus of variations, elliptic PDE, and algeb...(展开全部)

《紧黎曼曲面(第3版)(英文版)》主要内容包括：Uniformization of Compact Riemann Surfaces Geometric Structures on Riemann Surfaces、Preliminaries: Cohomology and Homology Groups、Harmonic and Holomorphic Differential Forms on Riemann Surfaces、The Periods of Holomorphic and Meromorphic Differential Forms、Divisors. The Riemann-Roch Theorem、Holomorphic 1-Forms and Metrics on Compact Riemann Surfaces、Divis...(展开全部)

This text covers Riemann surface theory from elementary aspects to the frontiers of current research. Open and closed surfaces are treated with emphasis on the compact case, while basic tools are developed to describe the analytic, geometric, and algebraic properties of Riemann surfaces and the associated Abelian varities. Topics covered include existence of meromorphic functio...(展开全部)

This introduction provides a highly readable critical overview of the main arguments and themes in twentieth--century and contemporary metaethics. It traces the development of contemporary debates in metaethics from their beginnings in the work of G. E. Moore up to the most recent arguments between naturalism and non--naturalism, cognitivism and non--cognitivism. * A highly rea...(展开全部)

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, som...(展开全部)

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 i...(展开全部)