Translation of "Riemann surface" in German

For formula_4 the Riemann surface has formula_5 parameters (the "moduli").

A Riemann surface X is a connected complex manifold of complex dimension one.

For example, the Riemann-Roch theorem (Roch was a student of Riemann) says something about the number of linearly independent differentials (with known conditions on the zeros and poles) of a Riemann surface.

In order to make this precise, define a stable map to be a pseudoholomorphic map from a Riemann surface with at worst nodal singularities, such that there are only finitely many automorphisms of the map.

For example, the Riemann–Roch theorem (Roch was a student of Riemann) says something about the number of linearly independent differentials (with known conditions on the zeros and poles) of a Riemann surface.

For g > 1 {\displaystyle g>1} the Riemann surface has ( 3 g ? 3 ) {\displaystyle (3g-3)} parameters (the "moduli").

The elements of L {\displaystyle L} are algebraic functions on a Riemann surface, a global object.

A smooth component of a nodal Riemann surface is said to be stable if there are at most finitely many automorphisms preserving its marked and nodal points.

Selberg used his trace formula to prove that the "Selberg zeta function" of a Riemann surface satisfies an analogue of the Riemann hypothesis.

In 1879 he looked at the action of PSL (2,7), thought of as an image of the modular group, and obtained an explicit representation of a Riemann surface.

He examined multi-valued functions as single valued over a special Riemann surface and solved general inversion problems which had been solved for elliptic integrals by Abel and Jacobi .

Clifford also proved that a Riemann surface is topologically equivalent to a box with holes in it.

In the early 1960s, Bers and Ahlfors showed that the space of conformal structures on a given Riemann surface can be modelled on a Banach space with a real analytic structure.

In this paper she constructed a fundamental polygon for the Fuchsian group representing a marked Riemann surface.

Speiser worked on number theory, group theory, and the theory of Riemann surfaces.

Other highlights include his work on abelian functions and theta functions on Riemann surfaces.

He works on hyperbolic geometry, Riemann surfaces and complex dynamics.

He studied the order of connectivity of Riemann surfaces.

Riemann Surfaces and Related Topics: Proceedings of the 1978 Stony Brook Conference.

He constructed from M5-branes, which are wound around Riemann surfaces with punctures.

These theories depended on the properties of a function defined on Riemann surfaces.

For the proof of the existence of functions on Riemann surfaces he used a minimality condition, which he called the Dirichlet principle.

Other eponymous honors are Zalcman domains, which play a role in the classification of Riemann surfaces, and Zalcman functions in complex dynamics.

His research deals with Riemann surfaces, quadratic differentials, Teichmüller spaces, hyperbolic geometry of surfaces and 3-manifolds, Fuchsian groups, Kleinian groups, complex dynamics, and low-dimensional geometric analysis.