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Asymptotically flat manifolds and cone structure at infinity
Anton Petrunin and Wilderich Tuschmann
Let M be an asymptotically flat m-manifold which has cone structure at infinity. We show that M has a finite number of ends and classify for simply connected ends all possible cones at infinity (except for dim M=4 where it is not clear if one of the theoretically possible cones can actually arise). This leads in particular to a classification of asymptotically flat nonnegatively curved manifolds: The universal covering of an asymptotically flat m-manifold with nonnegative sectional curvature is isometric to Rm-2 x M2, where M2 is an asymptotically flat surface.