Geodesic
A separating spherical belt with maximal radius ratio
Zapiski Nauchnykh Seminarov POMI, Geometry and topology. Part 3, Tome 252 (1998), pp. 13-20

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For compacta $A$, $B_ R^n$, given are the necessary and sufficient conditions for the spherical belt separating $A$ and $B$ and having the maximal ratio of the exterior and interior radii. 
@article{ZNSL_1998_252_a1,
     author = {V. A. Zalgaller},
     title = {A separating spherical belt with maximal radius ratio},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {13--20},
     publisher = {mathdoc},
     volume = {252},
     year = {1998},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1998_252_a1/}
}
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V. A. Zalgaller. A separating spherical belt with maximal radius ratio. Zapiski Nauchnykh Seminarov POMI, Geometry and topology. Part 3, Tome 252 (1998), pp. 13-20. http://geodesic.mathdoc.fr/item/ZNSL_1998_252_a1/