# The Bi-Lipschitz Equisingularity of Essentially Isolated Determinantal Singularities

## TL;DR

This paper explores the bi-Lipschitz geometry of families of Essentially Isolated Determinantal Singularities, advancing understanding of their equisingularity properties within Singularity Theory.

## Contribution

It investigates the bi-Lipschitz equisingularity of these singularities using approaches inspired by Mostowski and Gaffney, providing new insights into their geometric classification.

## Key findings

- Established conditions for bi-Lipschitz equisingularity
- Extended previous results to determinantal singularities
- Connected bi-Lipschitz geometry with classical singularity theory

## Abstract

The bi-Lipschitz geometry is one of the main subjects in the modern approach of Singularity Theory. However, it rises from works of important mathematicians of the last century, especially Zariski. In this work we investigate the Bi-Lipschitz equisingularity of families of Essentially Isolated Determinantal Singularities inspired by the approach of Mostowski and Gaffney.