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On monotonicity of the hypersphere volume and area

Abstract.

Motivated by reference [6] and applications in signal processing for communications systems, in this note, we obtain the dimension of maximum volume and the dimension of maximum surface area for the hypersphere of constant radius.

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Correspondence to Pavel Loskot.

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Loskot, P., Beaulieu, N.C. On monotonicity of the hypersphere volume and area. J. geom. 87, 96–98 (2007). https://doi.org/10.1007/s00022-007-1891-1

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  • DOI: https://doi.org/10.1007/s00022-007-1891-1

Mathematics Subject Classification (2000):

  • 51M20
  • 51M25

Keywords:

  • n-sphere
  • surface area
  • volume