%0 Journal Article
%T A new mass for asymptotically flat manifolds
%A Yuxin Ge
%A Guofang Wang
%A Jie Wu
%J Mathematics
%D 2012
%I arXiv
%X In this paper we introduce a mass for asymptotically flat manifolds by using the Gauss-Bonnet curvature. We first prove that the mass is well-defined and is a geometric invariant, if the Gauss-Bonnet curvature is integrable and the decay order $\tau$ satisfies $\tau > \frac {n-4}{3}.$ Then we show a positive mass theorem for asymptotically flat graphs over ${\mathbb R}^n$. Moreover we obtain also Penrose type inequalities in this case.
%U http://arxiv.org/abs/1211.3645v2