Surface area and other measures of ellipsoids

@article{Rivin2007SurfaceAA,
  title={Surface area and other measures of ellipsoids},
  author={Igor Rivin},
  journal={Adv. Appl. Math.},
  year={2007},
  volume={39},
  pages={409-427}
}
  • Igor Rivin
  • Published 2007
  • Mathematics, Computer Science
  • Adv. Appl. Math.
We begin by studying the surface area of an ellipsoid in E^n as the function of the lengths of the semi-axes. We give an explicit formula as an integral over S^n^-^1, use this formula to derive convexity properties of the surface area, to give sharp estimates for the surface area of a large-dimensional ellipsoid, to produce asymptotic formulas for the surface area and the isoperimetric ratio of an ellipsoid in large dimensions, and to give an expression for the surface in terms of the… Expand
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