Asymptotically flat and regular Cauchy data

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I describe the construction of a large class of asymptotically flat initial data with non-vanishing mass and angular momentum for which the metric and the extrinsic curvature have asymptotic expansions at space-like infinity in terms of powers of a radial coordinate. I emphasize the motivations and the main ideas behind the proofs.
22 pages, 14 figures in eps format, LaTeX 2e, springer style files. To appear in the proceedings of the Tuebingen conference on conformal structure of space-time, J. Frauendiener, H. Friedrich, eds, Springer Lecture Notes in Physics

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