05062nam 22014055 450 991015475010332120190708092533.01-4008-8190-010.1515/9781400881901(CKB)3710000000622812(SSID)ssj0001651270(PQKBManifestationID)16425628(PQKBTitleCode)TC0001651270(PQKBWorkID)13478734(PQKB)11147871(MiAaPQ)EBC4738777(DE-B1597)468037(OCoLC)979780957(DE-B1597)9781400881901(EXLCZ)99371000000062281220190708d2016 fg engurcnu||||||||txtccrThe Equidistribution Theory of Holomorphic Curves. (AM-64), Volume 64 /Hung-his WuPrinceton, NJ : Princeton University Press, [2016]©19701 online resource (252 pages) illustrationsAnnals of Mathematics Studies ;254Bibliographic Level Mode of Issuance: Monograph0-691-08073-9 Includes bibliographical references and index.Frontmatter -- PREFACE -- INTRODUCTION -- CONTENTS -- Chapter I. Generalities on projective spaces and Grassmannians -- Chapter II. Nevanlinna theory of meromorphic functions -- Chapter III. Elementary properties of holomorphic curves -- Chapter IV. The two main theorems for holomorphic curves -- Chapter V. The defect relations -- References -- Index of principal definitionsThis work is a fresh presentation of the Ahlfors-Weyl theory of holomorphic curves that takes into account some recent developments in Nevanlinna theory and several complex variables. The treatment is differential geometric throughout, and assumes no previous acquaintance with the classical theory of Nevanlinna. The main emphasis is on holomorphic curves defined over Riemann surfaces, which admit a harmonic exhaustion, and the main theorems of the subject are proved for such surfaces. The author discusses several directions for further research.Annals of mathematics studies ;no. 64.Value distribution theoryAnalytic functionsFunctions, MeromorphicAddition.Algebraic curve.Algebraic number.Atlas (topology).Binomial coefficient.Cauchy–Riemann equations.Compact Riemann surface.Compact space.Complex manifold.Complex projective space.Computation.Continuous function (set theory).Covariant derivative.Critical value.Curvature form.Diagram (category theory).Differential form.Differential geometry of surfaces.Differential geometry.Dimension.Divisor.Essential singularity.Euler characteristic.Existential quantification.Fiber bundle.Gaussian curvature.Geodesic curvature.Geometry.Grassmannian.Harmonic function.Hermann Weyl.Hermitian manifold.Holomorphic function.Homology (mathematics).Hyperbolic manifold.Hyperplane.Hypersurface.Improper integral.Intersection number (graph theory).Isometry.Line integral.Manifold.Meromorphic function.Minimal surface.Nevanlinna theory.One-form.Open problem.Open set.Orthogonal complement.Parameter.Picard theorem.Product metric.Q.E.D.Remainder.Riemann sphere.Riemann surface.Smoothness.Special case.Submanifold.Subset.Tangent space.Tangent.Theorem.Three-dimensional space (mathematics).Unit circle.Unit vector.Vector field.Volume element.Volume form.Value distribution theory.Analytic functions.Functions, Meromorphic.517.5Wu Hung-his, 1208697DE-B1597DE-B1597BOOK9910154750103321The Equidistribution Theory of Holomorphic Curves. (AM-64), Volume 642788682UNINA