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- W2950873250 abstract "The paper consists of two parts. In the first part, by using the Gauss-Bonnet curvature, which is a natural generalization of the scalar curvature, we introduce a higher order mass, the Gauss-Bonnet-Chern mass $m^{H}_k$, for asymptotically hyperbolic manifolds and show that it is a geometric invariant. Moreover, we prove a positive mass theorem for this new mass for asymptotically hyperbolic graphs and establish a relationship between the corresponding Penrose type inequality for this mass and weighted Alexandrov-Fenchel inequalities in the hyperbolic space $H^n$. In the second part, we establish these weighted Alexandrov-Fenchel inequalities in $H^n$ for any horospherical convex hypersurface $Sigma$. As an application, we obtain an optimal Penrose type inequality for the new mass defined in the first part for asymptotically hyperbolic graphs with a horizon type boundary $Sigma$, provided that a dominant energy condition $tilde L_kge0$ holds. Both inequalities are optimal." @default.
- W2950873250 created "2019-06-27" @default.
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- W2950873250 date "2013-06-18" @default.
- W2950873250 modified "2023-10-03" @default.
- W2950873250 title "The GBC mass for asymptotically hyperbolic manifolds" @default.
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- W2950873250 doi "https://doi.org/10.48550/arxiv.1306.4233" @default.
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