Rado's paracompactness theorem for conformal manifolds

TL;DR

This paper proves that all manifolds of dimension two or higher with a conformal structure are necessarily paracompact, extending understanding of the topological properties of conformal manifolds.

Contribution

The paper establishes that conformal structures on manifolds of dimension at least two imply paracompactness, a significant topological property, which was previously not fully understood.

Findings

Manifolds of dimension ≥ 2 with conformal structures are paracompact.

The result generalizes Rado's theorem to conformal manifolds.

Provides a foundational topological property for conformal geometry.

Abstract

We prove that every manifold of dimension $\ge 2$ admitting a conformal structure is paracompact.