# Riemann Uniformization Theorem

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## Theorem

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

This article is incomplete.In particular: More precise statementYou can help $\mathsf{Pr} \infty \mathsf{fWiki}$ by expanding it.To discuss this page in more detail, feel free to use the talk page.When this work has been completed, you may remove this instance of `{{Stub}}` from the code.If you would welcome a second opinion as to whether your work is correct, add a call to `{{Proofread}}` the page. |

## Proof

This theorem requires a proof.You can help $\mathsf{Pr} \infty \mathsf{fWiki}$ by crafting such a proof.To discuss this page in more detail, feel free to use the talk page.When this work has been completed, you may remove this instance of `{{ProofWanted}}` from the code.If you would welcome a second opinion as to whether your work is correct, add a call to `{{Proofread}}` the page. |

## 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