# Geometric rigidity of a class of fractal sets

## TL;DR

This paper investigates the geometric rigidity of a broader class of fractals than self-conformal sets, establishing conditions under which these fractals are either contained in smooth manifolds or are highly dispersed.

## Contribution

Introduces a new method to analyze the geometric rigidity of an extended class of fractals beyond self-conformal sets.

## Key findings

- Fractals are either contained in smooth submanifolds or are totally spread out.
- A new analytical approach to fractal rigidity is developed.
- The results extend known rigidity properties to a larger class of fractals.

## Abstract

We study geometric rigidity of a class of fractals, which is slightly larger than the collection of self-conformal sets. Namely, using a new method, we shall prove that a set of this class is contained in a smooth submanifold or is totally spread out.