2025/12/24 by Nikita Kalinin, Kalinin, Nikita, Mikhail Shkolnikov +1
Computer Science · Mathematics · Medicine · #14T05 #52A38 #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry (math.AG) #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Number Theory (math.NT) #Polynomial and algebraic computation #Spinal Hematomas and Complications
paper · doi:10.48550/arxiv.2512.21154
openalex publication_date 2025/12/24 · openalex created_date 2025/12/26 · openalex updated_date 2026/07/28
In this note, we introduce equi-affine invariants by averaging over the space of tropical structures of fixed covolume. Applied to the tropical distance series, this construction produces a family of equi-affine invariant functions associated with convex domains which are expected to satisfy a number of remarkable properties. We conjecture a limiting description of the associated level sets in the compact case, and we prove an analogue of this statement for unbounded domains with two non-parallel asymptotes. In addition, we give an explicit formula for the arithmetic mean value at the center of the unit disk.