parabolic cusp
1Cusp neighborhood — In mathematics, a cusp neighborhood is defined as a set of points near a cusp. Cusp neighborhood for a Riemann surface The cusp neighborhood for a hyperbolic Riemann surface can be defined in terms of its Fuchsian model. Suppose that the Fuchsian …
2Parabolic induction — In mathematics, parabolic induction is a method of constructing representations of a reductive group from representations of its parabolic subgroups. If G is a reductive algebraic group and P=MAN is the Langlands decomposition of a parabolic… …
3Cusp form — In number theory, a branch of mathematics, a cusp form is a particular kind of modular form, distinguished in the case of modular forms for the modular group by the vanishing in the Fourier series expansion (see q expansion) Σanqn of the constant …
4Katastrophentheorie (Mathematik) — Die mathematische Katastrophentheorie beschäftigt sich mit unstetigen, sprunghaften Veränderungen von bestimmten dynamischen Systemen. Diese können, auch wenn sie unter bestimmten Voraussetzungen einen stabilen Zustand anstreben, bei Änderungen… …
5Catastrophe theory — This article refers to the study of dynamical systems. For other meanings, see catastrophe. In mathematics, catastrophe theory is a branch of bifurcation theory in the study of dynamical systems; it is also a particular special case of more… …
6Gauss map — In differential geometry, the Gauss map (named after Carl F. Gauss) maps a surface in Euclidean space R3 to the unit sphere S 2. Namely, given a surface X lying in R3, the Gauss map is a continuous map N : X → S 2 such that N ( p ) is a unit… …
7Orbifold — This terminology should not be blamed on me. It was obtained by a democratic process in my course of 1976 77. An orbifold is something with many folds; unfortunately, the word “manifold” already has a different definition. I tried “foldamani”,… …
8Riemann surface — For the Riemann surface of a subring of a field, see Zariski–Riemann space. Riemann surface for the function ƒ(z) = √z. The two horizontal axes represent the real and imaginary parts of z, while the vertical axis represents the real… …
9Modular form — In mathematics, a modular form is a (complex) analytic function on the upper half plane satisfying a certain kind of functional equation and growth condition. The theory of modular forms therefore belongs to complex analysis but the main… …
10Cuspidal representation — In number theory, cuspidal representations are certain representations of algebraic groups that occur discretely in L2 spaces. The term cuspidal is derived, at a certain distance, from the cusp forms of classical modular form theory. In the… …
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