Geometry of Non-Archimedean Gromov-Hausdorff distance

TL;DR

This paper explores the geometric properties of the non-Archimedean Gromov-Hausdorff metric, aiming to connect it with number theory and p-adic analysis for potential new insights.

Contribution

It establishes foundational facts about the non-Archimedean Gromov-Hausdorff geometry, a novel area linking metric geometry with number theory.

Findings

Initial geometric properties of non-Archimedean Gromov-Hausdorff space

Potential relations between non-Archimedean geometry and p-adic number theory

Framework for future studies connecting geometry and arithmetic

Abstract

In this paper, we study the geometry of non-Archimedean Gromov-Hausdorff metric. This is the first part of our series work, which we try to establish some facts about the counterpart of Gromov-Hausdorff metric in the non-Archimedean spaces. One of the motivation of this work is to find some implied relations between this geometry and number theory via p-adic analysis, so that we can use the former as a tool to study the relating arithmetic aspects.