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Water waves --- Capillarity. --- Surface tension. --- Tension superficielle. --- Capillarité. --- Vagues --- Mathematical models. --- Modèles mathématiques. --- Waves --- Capillarity --- Surface tension --- Surface phenomena --- Liquids --- Surface chemistry --- Surface energy --- Wetting --- Matter --- Physics --- Permeability --- Cycles --- Hydrodynamics --- Benjamin-Feir instability --- Mathematical models --- Properties --- Ondes --- Capillarité --- Tension superficielle --- Modèles mathématiques
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This text provides a definitive proof of global nonlinear stability of Minkowski space-time as a solution of the Einstein-Klein-Gordon equations of general relativity. Along the way, a novel robust analytical framework is developed, which extends to more general matter models.
General relativity (Physics). --- Klein-Gordon equation. --- Mathematical physics. --- Quantum field theory. --- SCIENCE / Physics / Mathematical & Computational. --- Addition. --- Algebraic structure. --- Antiderivative. --- Approximation. --- Asymptote. --- Asymptotic analysis. --- Bending. --- Big O notation. --- Bootstrapping (statistics). --- Calculation. --- Cauchy distribution. --- Coefficient. --- Combination. --- Compact space. --- Complex number. --- Computation. --- Conserved quantity. --- Coordinate system. --- Coordinate-free. --- Covariant derivative. --- Derivative. --- Differential operator. --- Dispersion relation. --- Einstein field equations. --- Energy functional. --- Equation. --- Estimation. --- Exponential growth. --- Foliation. --- Fourier analysis. --- Fourier transform. --- Function (mathematics). --- Function space. --- General relativity. --- Geodesic. --- Geodesics in general relativity. --- Geographic coordinate system. --- Geometry. --- Global analysis. --- Globality. --- High frequency. --- Hyperboloid. --- Hypersurface. --- Hypothesis. --- Implementation. --- Ingredient. --- Integration by parts. --- Interpolation inequality. --- Klein–Gordon equation. --- Light cone. --- Local coordinates. --- Mathematical optimization. --- Metric tensor (general relativity). --- Metric tensor. --- Minkowski space. --- Momentum. --- Monograph. --- Monotonic function. --- Nonlinear system. --- Optics. --- Parametrization. --- Partial differential equation. --- Pointwise. --- Poisson bracket. --- Quantity. --- Remainder. --- Result. --- Riemann curvature tensor. --- Scalar field. --- Scattering. --- Schwarzschild metric. --- Scientific notation. --- Second fundamental form. --- Simultaneous equations. --- Small data. --- Small number. --- Sobolev space. --- Soliton. --- Space. --- Stability theory. --- Stress–energy tensor. --- Support (mathematics). --- Symmetrization. --- Theorem. --- Time derivative. --- Timelike Infinity. --- Trace (linear algebra). --- Two-dimensional space. --- Vacuum. --- Vector field. --- Very low frequency. --- Relativistic quantum field theory --- Field theory (Physics) --- Quantum theory --- Relativity (Physics) --- Physical mathematics --- Physics --- Schrödinger-Klein-Gordon equation --- Quantum field theory --- Wave equation --- Relativistic theory of gravitation --- Relativity theory, General --- Gravitation --- Mathematics --- General relativity (Physics) --- Science. --- Physics.
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"Princeton University's Elias Stein was the first mathematician to see the profound interconnections that tie classical Fourier analysis to several complex variables and representation theory. His fundamental contributions include the Kunze-Stein phenomenon, the construction of new representations, the Stein interpolation theorem, the idea of a restriction theorem for the Fourier transform, and the theory of Hp Spaces in several variables. Through his great discoveries, through books that have set the highest standard for mathematical exposition, and through his influence on his many collaborators and students, Stein has changed mathematics. Drawing inspiration from Stein's contributions to harmonic analysis and related topics, this volume gathers papers from internationally renowned mathematicians, many of whom have been Stein's students. The book also includes expository papers on Stein's work and its influence.The contributors are Jean Bourgain, Luis Caffarelli, Michael Christ, Guy David, Charles Fefferman, Alexandru Ionescu, David Jerison, Carlos Kenig, Sergiu Klainerman, Loredana Lanzani, Sanghyuk Lee, Lionel Levine, Akos Magyar, Detlef Müller, Camil Muscalu, Alexander Nagel, D. H. Phong, Malabika Pramanik, Andrew Raich, Fulvio Ricci, Keith Rogers, Andreas Seeger, Scott Sheffield, Luis Silvestre, Christopher Sogge, Jacob Sturm, Terence Tao, Christoph Thiele, Stephen Wainger, and Steven Zelditch"--
Mathematical analysis --- 3D. --- AKNS systems. --- Almgren minimal sets. --- Bergman kernels. --- Bochner–Riesz operator. --- Boltzmann equation. --- CTRW. --- Einstein equations. --- Einstein-vacuum equations. --- Eli Stein. --- Elias Stein. --- Fourier analysis. --- Fourier restriction operators. --- Fourier restriction. --- Fourier series. --- Fourier transform. --- Gagliardo–Nirenberg inequality. --- Gaussian Free Field. --- General Relativity. --- Hele-Shaw flow. --- Hp Spaces. --- Kunze–Stein phenomenon. --- Littlewood–Paley boundedness. --- Littlewood–Paley bounds. --- Littlewood–Paley theory. --- Newton polyhedra. --- Plateau's problem. --- Radon transform inequality. --- Radon transform. --- Radon transforms. --- Reifenberg. --- Stein interpolation theorem. --- Steiner symmetrization. --- admissible degree increment. --- affine group. --- applied mathematics. --- bounded L² curvature conjecture. --- classical Fourier analysis. --- continuous time random walks. --- convex hypersurfaces. --- correlated kernels. --- critical points. --- delicate Bessel. --- differential operators. --- div-curl. --- endpoint estimates. --- energy critical nonlinear wave equation. --- energy critical wave equation. --- evolution problems. --- extremizers. --- finite-type hypersurfaces. --- fluctuations. --- general polynomial maps. --- general polynomial sequences. --- geometric quasilinear equation. --- harmonic analysis. --- higher dimensions. --- higher order. --- holder regularity. --- inequalities. --- internal DLA. --- internal Diffusion-Limited Aggregation. --- lattice cylinder. --- martingales. --- mathematician. --- mathematics. --- maximal averages. --- maximal operators. --- model monomial domain. --- monomial-type domains. --- multi-linear multipliers. --- nilpotent lie groups. --- non-commutative nilpotent settings. --- oscillatory integral operators. --- oscillatory integrals. --- partial differential equations. --- polynomial sequences. --- pure mathematics. --- quasilinear hyperbolic system. --- radial Fourier multipliers. --- representation theory. --- rough kernels. --- selected theorems. --- simplexes. --- singular Radon transforms. --- size minimization problems. --- sliding minimal sets. --- soap films. --- soliton resolution. --- solitons. --- spherical maximal function. --- spherical measures. --- square functions. --- tri-linear operator.
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