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Teichmüller spaces --- Teichmüller, Espaces de --- Teichmüller spaces. --- Teichmüller spaces --- Teichmüller, Espaces de --- Teichmüller spaces.

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Differential geometry. Global analysis --- Teichmüller spaces. --- Geometry, Riemannian. --- Teichmüller, Espaces de --- Riemann, Géométrie de --- Teichmüller spaces. --- Teichmüller, Espaces de --- Riemann, Géométrie de

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Cluster algebras. --- Lambda algebra. --- Teichmüller spaces. --- Algèbres amassées --- Lambda-algèbre --- Espaces de Teichmüller --- Teichmüller, Espaces de --- Cluster algebras --- Lambda algebra --- Teichmüller spaces --- Algebras, Cluster --- Commutative algebra --- Spaces, Teichmüller --- Functions of several complex variables --- Riemann surfaces --- Algebra, Lambda --- Algebra, Homological --- Algèbres amassées. --- Teichmüller, Espaces de.

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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 algebraic geometry. It is unique among textbooks on Riemann surfaces in including an introduction to Teichmüller theory. The analytic approach is likewise new as it is based on the theory of harmonic maps.

Complex analysis --- Riemann surfaces. --- Riemann, surfaces de --- Riemann surfaces --- Mathematics --- Physical Sciences & Mathematics --- Calculus --- Geometry --- Teichmüller spaces. --- Teichmüller, Espaces de --- Differential geometry. --- Differential Geometry. --- Differential geometry --- Espaces analytiques --- Variétés complexes --- Analytic spaces --- Complex manifolds --- Surfaces, Riemann --- Functions --- Variétés complexes --- Teichmüller, Espaces de