# Exceptional rays and bilipschitz geometry of real surface singularities

## TL;DR

This paper investigates how the Nash cone and exceptional rays of real surface singularities in three-dimensional space behave under ambient bilipschitz transformations, expanding understanding of geometric invariants in singularity theory.

## Contribution

It analyzes the preservation and transformation of the Nash cone and exceptional rays under bilipschitz equivalence for real surface singularities, a novel focus in singularity geometry.

## Key findings

- Nash cone behavior under bilipschitz maps
- Exceptional rays' stability in singularities
- Insights into geometric invariants preservation

## Abstract

It is known that ambient bilipschitz equivalence preserves tangent cones. This paper explores the behavior of the Nash cone and, in particular, exceptional rays under ambient bilipschitz equivalence for real surfaces in $R^3$ with isolated singularity.