Comparison of invariant funcions and metrics

TL;DR

This paper demonstrates that all invariant metrics and functions on a bounded smooth domain agree on some open subset, highlighting a fundamental property of these mathematical objects.

Contribution

It establishes that all invariant metrics and functions of bounded smooth domains coincide on an open subset, revealing a key unifying property.

Findings

Invariant metrics and functions coincide on an open subset.

The result applies to bounded domains with smooth boundaries.

Highlights a fundamental property of invariant metrics and functions.

Abstract

In this short note it is shown that all invariant metrics and functions of bounded $\mathcal C^2$-smooth domain coincide on an open non-empty subset.