2024/07/06 by Rolf Schneider, Schneider, Rolf
Computer Science · Mathematics · #52A20 #Digital Image Processing Techniques #FOS: Mathematics #Metric Geometry (math.MG) #Point processes and geometric inequalities
paper · pdf · doi:10.48550/arxiv.2407.05095
openalex publication_date 2024/07/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A pseudo-cone in \mathbb Rn is a nonempty closed convex set K not containing the origin and such that λK ⊆ K for all λ≥ 1. It is called a C-pseudo-cone if C is its recession cone, where C is a pointed closed convex cone with interior points. The cone-volume measure of a pseudo-cone can be defined similarly as for convex bodies, but it may be infinite. After proving a necessary condition for cone-volume measures of C-pseudo-cones, we introduce suitable weights for cone-volume measures, yielding finite measures. Then we provide a necessary and sufficient condition for a Borel measure on the unit sphere to be the weighted cone-volume measure of some C-pseudo-cone.