✦ LIBER ✦

Zonoid theory and Hilbert's fourth problem

✍ Scribed by Ralph Alexander

Publisher: Springer
Year: 1988
Tongue: English
Weight: 597 KB
Volume: 28
Category: Article
ISSN: 0046-5755
DOI: 10.1007/bf00147451

No coin nor oath required. For personal study only.

✦ Synopsis

A finite vector sum of line segments is termed a zonotope. A zonoid is a Blaschke-Hausdorfflimit ofzonotopes. A projective metric d on a convex subset of projective space is shown to be of negative type if and only if the spheres in any tangent space are polar duals of zonoids. It follows that metric arclength can be represented by a Crofton formula with respect to a positive measure on the hyperplanes if and only if d is of negative type. These ideas allow a nice characterization of this cone of metrics.

📜 SIMILAR VOLUMES

Hilbert's tenth problem for weak theorie

Hilbert's tenth problem for weak theories of arithmetic

✍ Richard Kaye 📂 Article 📅 1993 🏛 Elsevier Science 🌐 English ⚖ 779 KB

Władysław Kretkowski and Hilbert's third

Władysław Kretkowski and Hilbert's third problem

✍ Walerian Piotrowski 📂 Article 📅 1985 🏛 Elsevier Science 🌐 English ⚖ 172 KB

Semidynamical systems and Hilbert’s fift

Semidynamical systems and Hilbert’s fifth problem

✍ J. W. Neuberger 📂 Article 📅 2008 🏛 Springer-Verlag 🌐 English ⚖ 809 KB

Hilbert's 17th Problem for Real Closed R

Hilbert's 17th Problem for Real Closed Rings

✍ Larry Mathews 📂 Article 📅 1994 🏛 John Wiley and Sons 🌐 English ⚖ 594 KB

## Abstract We recall the characterisation of positive definite polynomial functions over a real closed ring due to Dickmann, and give a new proof of this result, based upon ideas of Abraham Robinson. In addition we isolate the class of convexly ordered valuation rings for which this characterisati

Hilbert’s sixteenth problem and global b

Hilbert’s sixteenth problem and global bifurcations of limit cycles

✍ Valery A. Gaiko 📂 Article 📅 2001 🏛 Elsevier Science 🌐 English ⚖ 736 KB

TwistedL-Functions Over Number Fields an

TwistedL-Functions Over Number Fields and Hilbert’s Eleventh Problem

✍ Valentin Blomer; Gergely Harcos 📂 Article 📅 2010 🏛 Springer 🌐 English ⚖ 724 KB