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This book offers a systematic exposition of conformal methods and how they can be used to study the global properties of solutions to the equations of Einstein's theory of gravity. It shows that combining these ideas with differential geometry can elucidate the existence and stability of the basic solutions of the theory. Introducing the differential geometric, spinorial and PDE background required to gain a deep understanding of conformal methods, this text provides an accessible account of key results in mathematical relativity over the last thirty years, including the stability of de Sitter and Minkowski spacetimes. For graduate students and researchers, this self-contained account includes useful visual models to help the reader grasp abstract concepts and a list of further reading, making this the perfect reference companion on the topic.

General relativity (Physics) --- Geometry, Differential. --- Conformal mapping. --- Conformal geometry. --- Einstein field equations --- Space and time. --- Mathematics. --- Numerical solutions. --- 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 --- Hyperspace --- Relativity (Physics) --- Numerical analysis --- Circular geometry --- Geometry of inverse radii --- Inverse radii, Geometry of --- Inversion geometry --- Möbius geometry --- Geometry --- Conformal representation of surfaces --- Mapping, Conformal --- Transformation, Conformal --- Geometric function theory --- Mappings (Mathematics) --- Surfaces, Representation of --- Transformations (Mathematics) --- Differential geometry --- Relativistic theory of gravitation --- Relativity theory, General --- Gravitation --- Physics