# Riemann Uniformization Theorem

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## Theorem

Every connected $2$-dimensional manifold has a complete Riemannian metric with the constant Gaussian curvature.

## Proof

## Source of Name

This entry was named for Georg Friedrich Bernhard Riemann.

## Sources

- 2018: John M. Lee:
*Introduction to Riemannian Manifolds*(2nd ed.) ... (previous) ... (next): $\S 1$: What Is Curvature? Surfaces in Space