2003/06/04 by Igor Rivin, Rivin, Igor
Mathematics · #11P21 #52A38 #FOS: Mathematics #Metric Geometry (math.MG) #Number Theory (math.NT) #math.MG #math.NT #msc:11P21 #msc:52A38
paper · pdf · doi:10.48550/arxiv.math/0306085
arxiv created 2003/07/18 · arxiv updated 2009/11/30
We write down estimates for the surface area, and more generally, integral mean curvatures of an ellipsoid E in n-dimensional Euclidean space in terms of the lengths of the major semi-axes. We give applications to estimating the area of parallel surfaces and volume of the tubular neighborhood of E, to the counting of lattice points contained in E and to estimating the shape of the John ellipsoid of a convex body.