A new mass for asymptotically flat manifolds

作者：Ge Yuxin^*; Wang Guofang; Wu Jie

来源：Advances in Mathematics, 2014, 266: 84-119.

DOI：10.1016/j.aim.2014.08.006

• Gauss-Bonnet curvature
• Asymptotically flat manifolds
• Positive mass theorem
• Penrose inequalities

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 %26gt; n-4/3 Motivated by an elegant idea of Lam [35], we then show a positive mass theorem for this new mass for asymptotically fiat graphs over R-n. Moreover we obtain various Penrose type inequalities in this case. In these Penrose type inequalities we establish relationship between the new mass and various geometric integrals.

• 出版日期2014-12-1
• 单位中国科学技术大学