• Corpus ID: 250089015

Intrinsic volumes of ellipsoids

  title={Intrinsic volumes of ellipsoids},
  author={Anna Gusakova and E. Spodarev and Dmitry Zaporozhets},
. We deduce explicit formulae for the intrinsic volumes of an ellipsoid in R d , d ≥ 2, in terms of elliptic integrals. Namely, for an ellipsoid E ⊂ R d with semiaxes a 1 , . . . , a d we show that for all k = 1 , . . . , d , where s k − 1 is the ( k − 1)-th elementary symmetric polynomial and κ k is the volume of the k -dimensional unit ball. Some examples of the intrinsic volumes V k with low and high k are given where our formulae look particularly simple. As an application we derive new… 



Surface area and other measures of ellipsoids

Lower and Upper Bounds for Chord Power Integrals of Ellipsoids

First we discuss dierent representations of chord power integrals Ip(K) of any order p 0 for convex bodies K R d with inner points. Second we derive closed-term expressions of Ip(E(a)) for an

Intrinsic volumes of Sobolev balls with applications to Brownian convex hulls

A formula due to Sudakov relates the first intrinsic volume of a convex set in a Hilbert space to the maximum of the isonormal Gaussian process over this set. Using this formula we compute the first

Unique Determination of Ellipsoids by Their Dual Volumes

Gusakova and Zaporozhets conjectured that ellipsoids in $\mathbb R^n$ are uniquely determined (up to an isometry) by their Steiner polynomials. Petrov and Tarasov confirmed this conjecture in

The distance between two random points in plane regions

  • T. Sheng
  • Mathematics
    Advances in Applied Probability
  • 1985
Let T be a triangle. P be a parallelogram, E be an ellipse, A , B be concentric circles, C , D be concentric dartboard regions, R , S be rectangles of the same orientation, U, V be two finite unions

The moments of the distance between two random points in a regular polygon

In this paper, we derive formulas for the analytical calculation of the moments of the distance between two uniformly and independently distributed random points in an n-sided regular polygon. A

Uniqueness of a Three-Dimensional Ellipsoid with Given Intrinsic Volumes

Let $${\mathcal {E}}$$ E be an ellipsoid in $${\mathbb {R}}^n$$ R n . Gusakova and Zaporozhets conjectured that $${\mathcal {E}}$$ E is uniquely (up to rigid motions) determined by its intrinsic

The Expected Volume of a Tetrahedron whose Vertices are Chosen at Random in the Interior of a Cube

Abstract. We calculate E[V4(C)], the expected volume of a tetrahedron whose vertices are chosen randomly (i.e. independently and uniformly) in the interior of C, a cube of unit volume. We find$$E[V_4