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- W2080342127 abstract "We consider asymptotically flat manifolds of the form $(S^3 setminus { P }, G^4 g)$, where $G$ is the Green's function of the conformal Laplacian of $(S^3, g)$ at a point $P$. We show if $Ric(g) geq 2 g$ and the volume of $(S^3, g)$ is no less than one half of the volume of the standard unit sphere, then there are no closed minimal surfaces in $(S^3 setminus { P }, G^4 g)$. We also give an example of $(S^3, g)$ where $Ric(g) > 0$ but $(S^3 setminus { P }, G^4 g)$ does have closed minimal surfaces." @default.
- W2080342127 created "2016-06-24" @default.
- W2080342127 creator A5051533068 @default.
- W2080342127 date "2007-01-01" @default.
- W2080342127 modified "2023-10-16" @default.
- W2080342127 title "A Note on Existence and Non-existence of Horizons in Some Asymptotically Flat $3$-manifolds" @default.
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- W2080342127 doi "https://doi.org/10.4310/mrl.2007.v14.n3.a4" @default.
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