A new mass for asymptotically flat manifolds

Yuxin Ge; Guofang Wang; Jie Wu

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arXiv · 1211.3645

A new mass for asymptotically flat manifolds

Yuxin Ge·Guofang Wang·Jie Wu

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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 $τ$ satisfies $τ> \frac {n-4}{3}.$ 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.

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Yuxin Ge, Guofang Wang, Jie Wu. 2013-04-29. A new mass for asymptotically flat manifolds. https://arxiv.org/abs/1211.3645

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