Borel fixed-point theorem
In mathematics, the Borel fixed-point theorem is a fixed-point theorem in algebraic geometry generalizing the Lie–Kolchin theorem. The result was proved by Armand Borel (1956).
If G is a ...
Borel fixed-point theorem - Wikipedia
Reider's theorem
In algebraic geometry, Reider's theorem gives conditions for a line bundle on a projective surface to be very ample.
Suppose that L is a line bundle on a smooth projective surface with canonical b...
Circle packing theorem
The circle packing theorem (also known as the Koebe–Andreev–Thurston theorem) describes the possible tangency relations between circles in the plane whose interiors are disjoint. A circle packing is...
Circle packing theorem - Wikipedia
Campbell's theorem (geometry)
Campbell's theorem, also known as Campbell’s embedding theorem and the Campbell-Magaarrd theorem, is a mathematical theorem that evaluates the asymptotic distribution of random impulses acting with a ...
Niven's theorem
In mathematics, Niven's theorem, named after Ivan Niven, states that the only rational values of θ in the interval 0 ≤ θ ≤ 90 for which the sine of θ degrees i...
Niven's theorem - Wikipedia
Atiyah–Singer index theorem
In differential geometry, the Atiyah–Singer index theorem, proved by Michael Atiyah and Isadore Singer (1963), states that for an elliptic differential operator on a compact manifold,...
Birkhoff–Grothendieck theorem
In mathematics, the Birkhoff–Grothendieck theorem classifies holomorphic vector bundles over the complex projective line. In particular every holomorphic vector bundle over is a direct sum of holomor...
Birkhoff–Grothendieck theorem - Wikipedia
Loomis–Whitney inequality
In mathematics, the Loomis–Whitney inequality is a result in geometry, which in its simplest form, allows one to estimate the "size" of a d-dimensional set by the sizes of its (d – 1)-dimensiona...
Abhyankar–Moh theorem
In mathematics, the Abhyankar–Moh theorem states that if is a complex line in the complex affine plane , then every embedding of into extends to an automorphism of the plane. It is named after Shre...
Mnev's universality theorem
In algebraic geometry, Mnev's universality theorem is a result which can be used to represent algebraic (or semi algebraic) varieties as realizations of oriented matroids, a notion of combinatorics.
Hsiang-Lawson's conjecture
In mathematics, Lawson's conjecture states that the Clifford torus is the only minimally embedded torus in the 3-sphere S. The conjecture was featured by the Australian Mathematical Society Gazette as...
Saccheri–Legendre theorem
In absolute geometry, the Saccheri–Legendre theorem asserts that the sum of the angles in a triangle is at most 180°. Absolute geometry is the geometry obtained from assuming all the axioms that lead ...
Addition theorem
In mathematics, an addition theorem is a formula such as that for the exponential functionthat expresses, for a particular function f, f(x + y) in terms of f(x) and f(y). Slightly more generally, as i...
Pick's theorem
Given a simple polygon constructed on a grid of equal-distanced points (i.e., points with integer coordinates) such that all the polygon's vertices are grid points, Pick's theorem provides a simple fo...
Pick's theorem - Wikipedia
Steiner-Lehmus theorem
The Steiner–Lehmus theorem, a theorem in elementary geometry, was formulated by C. L. Lehmus and subsequently proved by Jakob Steiner. It states:The theorem was first mentioned in 1840 in a letter by ...
Mukhopadhyaya theorem
In geometry Mukhopadhyaya's theorem may refer to one of several closely related theorems about the number of vertices of a curve due to Mukhopadhyaya (1909). One version, called the Four-vertex t...
Mukhopadhyaya theorem - Wikipedia
Poncelet–Steiner theorem
In Euclidean geometry, the Poncelet–Steiner theorem concerning compass and straightedge constructions states that whatever can be constructed by straightedge and compass together can be constructed by...
Poncelet–Steiner theorem - Wikipedia
Pasch's theorem
In geometry, Pasch's theorem, stated in 1882 by the German mathematician Moritz Pasch, is a result of Euclidean geometry which cannot be derived from Euclid's postulates.The statement is as follows. G...
Dévissage
In algebraic geometry, dévissage is a technique introduced by Alexander Grothendieck for proving statements about coherent sheaves on noetherian schemes. Dévissage is an adaptation of a certain kind o...
Reshetnyak gluing theorem
In metric geometry, the Reshetnyak gluing theorem gives information on the structure of a geometric object build by using as building blocks other geometric objects, belonging to a well defined class....