Inequalities for mixedp-affine surface area
β Scribed by Elisabeth Werner; Deping Ye
- Publisher
- Springer
- Year
- 2009
- Tongue
- English
- Weight
- 400 KB
- Volume
- 347
- Category
- Article
- ISSN
- 0025-5831
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
We show that every upper semicontinuous and equi-affine invariant valuation on the space of d-dimensional convex bodies is a linear combination of affine surface area, volume, and the Euler characteristic.
## Abstract Let __K__ be a convex body in R__^d^__. A random polytope is the convex hull [x~1~, β¦, __x~n~__] of finitely many points chosen at random in __K__. IE(__K, n__) is the expectation of the volume of a random polytope of __n__ randomly chosen points. I. BΓ‘rΓ‘ny showed that we have for conve
bounded by the ellipsoid with principal axes of lengths 2a, 2b, and 2c, its surface area, S(a, b, c), is a non-elementary integral unless a = b = c, (E is a ball) or two values of a, b, and c are equal (E is a solid spheroid). This leads to upper and lower estimates for S(a, b, c) in terms of the su