Linked from

The 16 pages that link to Riemann surface, each with the reason it gives.

• Analytic continuationNarrower topic: It turns path-dependent continuation into ordinary function evaluation on a larger space.

• Complex logarithmNarrower topic: Its infinitely many sheets turn the logarithm’s separate values into one analytic function.

• Conformal mapNarrower topic: Conformal maps provide the natural equivalences between these complex surfaces.

• Uniformization theoremNarrower topic: Uniformization classifies these surfaces by identifying the conformal type of each simply connected one.

• Elliptic functionNarrower topic: The torus interpretation places elliptic functions within the broader theory of complex surfaces.

• Branch pointNarrower topic: Over this point, the surface’s sheets meet or ramify, representing the branch structure geometrically.

• Elliptic integralNarrower topic: A Riemann surface makes the branches of the polynomial square root part of one geometric object.

• Riemann–Hurwitz formulaNarrower topic: The formula arose within the study of maps between these complex surfaces.

• Cousin problemsNarrower topic: The classical problems first take shape as global function questions on complex curves.

• Behnke–Stein theoremNarrower topic: The theorem concerns the global analytic structure of its noncompact members.

• Harnack's curve theoremNarrower topic: A real plane curve sits inside a complex curve whose genus governs Harnack's bound.