A new mass for asymptotically flat manifolds

Abstract

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.

32 pages. arXiv:1211.7305 was integrated into this new version as an application

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Cited by in corpus (4)

• The Gauss-Bonnet-Chern mass for graphic manifolds
• A positive mass theorem in the Einstein-Gauss-Bonnet theory
• On Rigidity of hypersurfaces with constant curvature functions in warped product manifolds
• The GBC mass for asymptotically hyperbolic manifolds