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A σ2 Penrose inequality for conformal asymptotically hyperbolic 4-discs
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A σ2 Penrose inequality for conformal asymptotically hyperbolic 4-discs

Hao Fang and Wei Wei
Advances in mathematics (New York. 1965), Vol.402, 108365
06/25/2022
DOI: 10.1016/j.aim.2022.108365

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Abstract

Keywords [sigma] 2 Yamabe; Conic metric; Asymptotically hyperbolic; Mass inequality In this paper, we consider conformal flat metrics on R.sup.4 with an asymptotically hyperbolic (AH) end and possible isolated conic singularities. We define a mass term of the AH end. If the [sigma].sub.2 curvature has lower bound [sigma].sub.2[greater than or equal to]3/2, we prove an inequality relating the mass and contributions from singularities. We also classify sharp cases, which is the standard hyperbolic 4-space H.sup.4 when no singularity occurs. It is worth noting that our curvature condition implies non-positive energy density. Author Affiliation: (a) 14 MacLean Hall, Department of Mathematics, University of Iowa, Iowa City, IA, 52242, United States of America (b) Department of Mathematics, Nanjing University, Nanjing, 210093, PR China * Corresponding author. Article History: Received 27 May 2021; Revised 16 March 2022; Accepted 17 March 2022 (miscellaneous) Communicated by YanYan Li (footnote)[white star] H.F.'s work is partially supported by a Simons Foundation research collaboration grant No. 426312. W.W.'s work is partially supported by the Initiative postdoctoral fund of China (grant No. BX20190082). Byline: Hao Fang [hao-fang@uiowa.edu] (a), Wei Wei [wei_wei@nju.edu.cn] (b,*)
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