The Crofton Cup

Crofton Measures and Minkowski Valuations

A description of continuous rigid motion compatible Minkowski valuations is established. As an application we present a Brunn–Minkowski type inequality for intrinsic volumes of these valuations.

Crofton Formulas in Projective Finsler Spaces

We extend the classical Crofton formulas in Euclidean integral geometry to Finsler metrics on Rn whose geodesics are straight lines.

Note on the Bacteriology of the "Crofton Hall" Tragedy

Transcriptome profiling of the crofton weed gall fly Procecidochares utilis.

Procecidochares utilis is a tephritid gall fly, which is known to be an effective biological agent that can be used to control the notoriously widespread crofton weed Eupatorium adenophorum. Despite its importance, genetic resources for P. utilis remain scarce. In this study, 1.2 Gb sequences were generated using Illumina paired-end sequencing technology. De novo assemblies yielded 491,760 cont...

Crofton Measures in Polytopal Hilbert Geometries

The Hilbert geometry in an open bounded convex set in R is a classical example of a projective Finsler space. We construct explicitly a positive measure on the space of lines in a polytopal Hilbert geometry which yields an integral geometric representation of Crofton type for the Holmes-Thompson area of hypersurfaces. MSC 2000: 53C60 (primary); 53C65, 52B11 (secondary)