Geodesic
Equipartition of a mass continuously distributed on a sphere or in space
Zapiski Nauchnykh Seminarov POMI, Geometry and topology. Part 6, Tome 279 (2001), pp. 187-196

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Masses continuously distributed on a sphere or in a projective or Euclidean space are considered. Several theorems on equipartition of such a mass by a configuration of planes of this or other type are proved by topological means. Unsolved questions are posed. 
@article{ZNSL_2001_279_a11,
     author = {V. V. Makeev},
     title = {Equipartition of a mass continuously distributed on a sphere or in space},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {187--196},
     publisher = {mathdoc},
     volume = {279},
     year = {2001},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2001_279_a11/}
}
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V. V. Makeev. Equipartition of a mass continuously distributed on a sphere or in space. Zapiski Nauchnykh Seminarov POMI, Geometry and topology. Part 6, Tome 279 (2001), pp. 187-196. http://geodesic.mathdoc.fr/item/ZNSL_2001_279_a11/