MiS Preprint Repository

We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV ( that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint

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.


Related publications

2001 Repository Open Access
Anton Petrunin and Wilderich Tuschmann

Asymptotical flatness and cone structure at infinity

In: Mathematische Annalen, 321 (2001) 4, pp. 775-788