Surface Area of Ellipsoids
Metric Geometry
2007-05-23 v4 Probability
Abstract
We study the surface area of an ellipsoid in n-dimensional Euclidean space as the function of the lengths of their major semi-axes. We write down an explicit formula as an integral over the unit sphere, use the 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 in large dimensions, and to give an expression for the surface in terms of the Lauricella hypergeometric function.
Keywords
Cite
@article{arxiv.math/0306387,
title = {Surface Area of Ellipsoids},
author = {Igor Rivin},
journal= {arXiv preprint arXiv:math/0306387},
year = {2007}
}
Comments
simplified version with essentially optimal estimates