On direct and inverse limits of Minkowski's balls, domains, and their critical lattices

TL;DR

This paper constructs and analyzes direct and inverse systems of Minkowski's balls, domains, and their critical lattices, calculating their limits to understand their structural properties.

Contribution

It introduces a framework for constructing and computing limits of systems involving Minkowski's balls, domains, and critical lattices, providing new insights into their geometric and lattice structures.

Findings

Calculated explicit limits of Minkowski's balls and domains

Established relationships between critical lattices and geometric limits

Provided a systematic approach to analyze lattice structures in convex geometry

Abstract

We construct direct and inverse systems of Minkowski's balls and domains, direct and inverse systems of their critical lattices and calculate their direct and inverse limits.