Tropical measures, anisotropic isoperimetric inequality and honeycomb
Abstract
We introduce a tropical spherical measure on $\mathbb{R}^n$ that is based on the tropical metric and is an analogue of spherical Hausdorff measure. This measure is translation invariant but, unlike Lebesgue measure, is not invariant under rotations or reflections. It agrees with Lebesgue measure on $n$-dimensional (but not on $k$-dimensional, $k
Fields of Study & Subjects
Geometric Analysis and Curvature Flows
Point processes and geometric inequalities
Advanced Combinatorial Mathematics
Publication details
- Journal / source
- arXiv (Cornell University)
- Publication date
- 3 March 2026
- Language
- EN
- Document type
- Preprint