Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

This 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.

Analytic functions. --- Functions, Meromorphic. --- Value distribution theory. --- Meromorphic functions --- Functions, Analytic --- Functions, Monogenic --- Functions, Regular --- Regular functions --- Functions of complex variables --- Series, Taylor's --- Distribution of values theory --- Functions, Entire --- Functions, Meromorphic --- Addition. --- 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. --- Fonctions de plusieurs variables complexes

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

The aim of this work is to provide a proof of the nonlinear gravitational stability of the Minkowski space-time. More precisely, the book offers a constructive proof of global, smooth solutions to the Einstein Vacuum Equations, which look, in the large, like the Minkowski space-time. In particular, these solutions are free of black holes and singularities. The work contains a detailed description of the sense in which these solutions are close to the Minkowski space-time, in all directions. It thus provides the mathematical framework in which we can give a rigorous derivation of the laws of gravitation proposed by Bondi. Moreover, it establishes other important conclusions concerning the nonlinear character of gravitational radiation. The authors obtain their solutions as dynamic developments of all initial data sets, which are close, in a precise manner, to the flat initial data set corresponding to the Minkowski space-time. They thus establish the global dynamic stability of the latter.Originally published in 1994.The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.

Space and time --- Generalized spaces --- Nonlinear theories --- Physics --- Physical Sciences & Mathematics --- Atomic Physics --- Nonlinear problems --- Nonlinearity (Mathematics) --- Calculus --- Mathematical analysis --- Mathematical physics --- Geometry of paths --- Minkowski space --- Spaces, Generalized --- Weyl space --- Calculus of tensors --- Geometry, Differential --- Geometry, Non-Euclidean --- Hyperspace --- Relativity (Physics) --- Space of more than three dimensions --- Space-time --- Space-time continuum --- Space-times --- Spacetime --- Time and space --- Fourth dimension --- Infinite --- Metaphysics --- Philosophy --- Space sciences --- Time --- Beginning --- Mathematics --- Angular momentum operator. --- Asymptotic analysis. --- Asymptotic expansion. --- Big O notation. --- Boundary value problem. --- Cauchy–Riemann equations. --- Coarea formula. --- Coefficient. --- Compactification (mathematics). --- Comparison theorem. --- Corollary. --- Covariant derivative. --- Curvature tensor. --- Curvature. --- Cut locus (Riemannian manifold). --- Degeneracy (mathematics). --- Degrees of freedom (statistics). --- Derivative. --- Diffeomorphism. --- Differentiable function. --- Eigenvalues and eigenvectors. --- Eikonal equation. --- Einstein field equations. --- Equation. --- Error term. --- Estimation. --- Euclidean space. --- Existence theorem. --- Existential quantification. --- Exponential map (Lie theory). --- Exponential map (Riemannian geometry). --- Exterior (topology). --- Foliation. --- Fréchet derivative. --- Geodesic curvature. --- Geodesic. --- Geodesics in general relativity. --- Geometry. --- Hodge dual. --- Homotopy. --- Hyperbolic partial differential equation. --- Hypersurface. --- Hölder's inequality. --- Identity (mathematics). --- Infinitesimal generator (stochastic processes). --- Integral curve. --- Intersection (set theory). --- Isoperimetric inequality. --- Laplace's equation. --- Lie algebra. --- Lie derivative. --- Linear equation. --- Linear map. --- Logarithm. --- Lorentz group. --- Lp space. --- Mass formula. --- Mean curvature. --- Metric tensor. --- Minkowski space. --- Nonlinear system. --- Normal (geometry). --- Null hypersurface. --- Orthonormal basis. --- Partial derivative. --- Poisson's equation. --- Projection (linear algebra). --- Quantity. --- Radial function. --- Ricci curvature. --- Riemann curvature tensor. --- Riemann surface. --- Riemannian geometry. --- Riemannian manifold. --- Sard's theorem. --- Scalar (physics). --- Scalar curvature. --- Scale invariance. --- Schwarzschild metric. --- Second derivative. --- Second fundamental form. --- Sobolev inequality. --- Sobolev space. --- Stokes formula. --- Stokes' theorem. --- Stress–energy tensor. --- Symmetric tensor. --- Symmetrization. --- Tangent space. --- Tensor product. --- Theorem. --- Trace (linear algebra). --- Transversal (geometry). --- Triangle inequality. --- Uniformization theorem. --- Unit sphere. --- Vector field. --- Volume element. --- Wave equation. --- Weyl tensor.