Tom Baumbach

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math.MG2026

On the Solution Sets of the Cone-Volume Map

Tom Baumbach, Zhang Chen, Martin Henk

For a fixed set $U = (u_{1}, \dots, u_{m})$ of outer unit normals, we consider the cone-volume map which associates to a vector of support numbers $b \in R_{> 0}^{m}$ the cone-volume…

math.MG2026

On the discrete logarithmic Minkowski problem in the plane

Tom Baumbach

The paper characterizes the convex hull of the closure of the cone-volume set $C_\cv(U)$, consisting of all cone-volume vectors of polygons with outer unit normals vectors containe…

math.MG2025

On polynomial inequalities for cone-volumes of polytopes

Tom Baumbach, Martin Henk

Motivated by the discrete logarithmic Minkowski problem we study for a given matrix $U \in R^{n \times m}$ its cone-volume set $C_{cv} (U)$ consisting of all the cone-volu…