Category
page 1Theorems in convex geometry
Brouwer fixed-point theorem
every continuous function on a compact set has a fixed point
Minkowski addition
commutative associative binary operation on subsets of an Abelian group (such as Euclidean space)
Kakutani fixed-point theorem
theorem that a function f: S→Pow(S) on a compact nonempty convex subset S⊂ℝⁿ, whose graph is closed and whose image f(x) is nonempty and convex for all x∈S, has a fixed point
Krein–Milman theorem
theorem
Cauchy's theorem
theorem in geometry
Helly's theorem
theorem about the intersections of d-dimensional convex sets
Radon's theorem
theorem that d+2 points in d dimensions can be partitioned into two subsets whose convex hulls intersect
Brunn–Minkowski theorem
theorem in geometry
Carathéodory's theorem
theorem on convex hulls
maximum-margin hyperplane
convex polyhedra
Hadwiger's theorem
theorem in integral geometry
Tverberg's theorem
theorem in discrete geometry
Alexandrov's uniqueness theorem
rigidity theorem in mathematics