# Value range of solutions to the chordal Loewner equation with restriction on the driving function

## TL;DR

This paper investigates the value range of solutions to the chordal Loewner equation under bounded driving functions, employing reachable set methods and Pontryagin's maximum principle to analyze the problem.

## Contribution

It introduces a novel approach combining reachable set methods and Pontryagin's maximum principle to study the value range of solutions with restricted driving functions.

## Key findings

- Derived bounds for the value range of solutions
- Applied control theory techniques to complex analysis problems
- Provided new insights into the behavior of solutions with bounded driving functions

## Abstract

We consider a value range $\{g(i,T)\}$ of solutions to the chordal Loewner equation with the restriction $|\lambda(t)| \le c$ on the driving function. We use reachable set methods and the Pontryagin maximum principle.