Convex geometry

Branch of geometry In mathematics, convex geometry is the branch of geometry studying convex sets, mainly in Euclidean space. Convex sets occur naturally in many areas: computational geometry, convex analysis, discrete geometry, functional analysis, geometry of numbers, integral geometry, linear programming, probability theory, game theory, etc. Classification According to the Mathematics Subject Classification MSC2010, the mathematical discipline Convex and Discrete Geometry includes three major branches: general convexity polytopes and polyhedra discrete geometry (though only portions of the latter two are included in convex geometry). General convexity is further subdivided as follows: axiomatic and generalized convexity convex sets without dimension restrictions convex sets in topological vector spaces convex sets in 2 dimensions (including convex curves) convex sets in 3 dimensions (including convex surfaces) convex sets in n dimensions (including convex hypersurfaces) finite-dimensional Banach spaces random convex sets and integral geometry asymptotic theory of convex bodies approximation by convex sets variants of convex sets (star-shaped, (m, n)-convex, etc.) Helly-type the