Riemann Surfaces
Leo Sario, Lars Valerian Ahlfors
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Naturwissenschaften, Medizin, Informatik, Technik / Mathematik
Beschreibung
The theory of Riemann surfaces has a geometric and an analytic part. The former deals with the axiomatic definition of a Riemann surface, methods of construction, topological equivalence, and conformal mappings of one Riemann surface on another. The analytic part is concerned with the existence and properties of functions that have a special character connected with the conformal structure, for instance: subharmonic, harmonic, and analytic functions.
Originally published in 1960.
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Kundenbewertungen
Topological space, Positive harmonic function, Finite intersection property, Boundary (topology), Branch point, Open set, Principal value, Coefficient, Removable singularity, Heine–Borel theorem, Partition of unity, Triangle inequality, Uniformization theorem, Analytic function, Maximum principle, Projection (linear algebra), Jordan curve theorem, Orthogonal complement, Linear map, Skew-symmetric matrix, Subset, Green's function, Harmonic function, Infimum and supremum, Free group, Normal subgroup, Basis (linear algebra), Upper and lower bounds, Axiom of choice, Projection (mathematics), Compact space, Riemann surface, Bolzano–Weierstrass theorem, Unit disk, Uniform continuity, Isolated singularity, Coset, Upper half-plane, Metric space, Weyl's lemma (Laplace equation), Harmonic measure, Sign (mathematics), Normal operator, Ideal point, Extremal length, Dirichlet integral, Meromorphic function, Zorn's lemma, Existential quantification, Theorem, Riemann mapping theorem, Special case, Betti number, Simply connected space, Subgroup, Big O notation, Linear independence, Bounded set (topological vector space), Canonical basis, Homeomorphism, Disjoint union, Fundamental group, Topology, Maximal set, Orientability, Polyhedron, Support (mathematics), Characterization (mathematics), Limit point, Continuous function (set theory)