space is called geometrically finite if it has a well-behaved fundamental domain. A hyperbolic manifold is called geometrically finite if it can be described...

A finite geometry is any geometric system that has only a finite number of points. The familiar Euclidean geometry is not finite, because a Euclidean line...

A geometric progression, also known as a geometric sequence, is a mathematical sequence of non-zero numbers where each term after the first is found by...

Geometric group theory is an area in mathematics devoted to the study of finitely generated groups via exploring the connections between algebraic properties...

projection of affine n-space over U. f is flat, locally of finite presentation, and for every geometric point y ¯ {\displaystyle {\bar {y}}} of Y (a morphism...

the assumption of finiteness. Geometric lattices and matroid lattices, respectively, form the lattices of flats of finite, or finite and infinite, matroids...

in turn, special cases of geometric finite automata or topological finite automata. The automata work by receiving a finite-length string σ = ( σ 0 ,...

instruments used in most geometric constructions are the compass and straightedge. Also, every construction had to be complete in a finite number of steps. However...

structure of a hyperbolic 3-manifold of finite volume is uniquely determined by its homotopy type. In particular, geometric invariants such as the volume can...

Katz–Lang finiteness theorem, proved by Nick Katz and Serge Lang (1981), states that if X is a smooth geometrically connected scheme of finite type over...

condition of having a finitely-sided Dirichlet domain is no longer equivalent to the standard notions of geometric finiteness. In a subsequent paper...

In mathematics, a geometric series is a series summing the terms of an infinite geometric sequence, in which the ratio of consecutive terms is constant...

inherits some finiteness property of a space. Geometric group theory studies the connections between algebraic properties of finitely generated groups...

Ohshika (2011), states that every finitely generated Kleinian group is an algebraic limit of geometrically finite Kleinian groups. Bers (1970) suggested...

its tools and principles can be applied to sets of any finite dimension. Today most geometric modeling is done with computers and for computer-based applications...

proper, geodesic metric space. An action of a finitely-generated group G on a geometry X is geometric if it satisfies the following conditions: Each...

In mathematics, the geometric mean is a mean or average which indicates a central tendency of a finite collection of positive real numbers by using the...

In mathematics, geometric invariant theory (or GIT) is a method for constructing quotients by group actions in algebraic geometry, used to construct moduli...

geometric algebra (also known as a Clifford algebra) is an algebra that can represent and manipulate geometrical objects such as vectors. Geometric algebra...

infinite groups. Special cases of groups with finiteness properties are finitely generated and finitely presented groups. Given an integer n ≥ 1, a group...

Society. These questions significantly influenced the development of geometric topology and related fields over the following decades. The questions...

Computational geometry applies algorithms to geometrical problems and representations of geometrical objects, while computer image analysis applies...

generators. The Ahlfors finiteness theorem says that such a group is of finite type. A Kleinian group Γ has finite covolume if H3/Γ has finite volume. Any Kleinian...

algebras G {\displaystyle {\mathcal {G}}} (p, q). UGA contains all finite-dimensional geometric algebras (GA). The elements of UGA are called multivectors. Every...

Geometric analysis is a mathematical discipline where tools from differential equations, especially elliptic partial differential equations (PDEs), are...

In mathematics, the inequality of arithmetic and geometric means, or more briefly the AM–GM inequality, states that the arithmetic mean of a list of non-negative...

mathematics, geometric topology is the study of manifolds and maps between them, particularly embeddings of one manifold into another. Geometric topology...

every finitely generated Kleinian group is an algebraic limit of geometrically finite Kleinian groups, and was independently proven by Ohshika and Namazi–Souto...

probability distribution for the Bernoulli, binomial, negative binomial, and geometric distributions. The formulation of the beta distribution discussed here...

has four chapters, on braid groups, isoperimetric inequalities, geometric finiteness, and the fundamental groups of three-dimensional manifolds. Although...