A branch of geometry dealing with convex sets and functions. Polytopes, convex bodies, discrete geometry, linear programming, antimatroids, ...

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### Extreme points in $d$-dimensional quadrant hull of $n$ random points in a halfplane

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### Applying a piecewise linear function to vertices of a polytope while remaining in facet representation

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### Convex hull of piece-wise linear functions

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### Structures of the space of neural networks

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### Is the preimage of a face under an affine map a face?

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### Relative interior of subdifferential

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### Visual proof of convergence for Steiner's symmetrization

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### Is it possible to continuously select a probability distribution over fixed points in Brouwer's fixed point theorem?

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### Does this formula for caliper diameter hold for concave polyhedra?

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### Average caliper diameter (mean width) of a polyhedron

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### Ellipsoid minimizing Banach-Mazur distance to convex body

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### Choquet Theorem for the cone of non-negative operators

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### Cutting a convex body into two congruent pieces

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### Steiner's inequality reference request

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### Realisation of a Polytope as a convex set [duplicate]

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### Probability that the perturbed convex hull is larger than the original one

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### Is the level set of a product of affine linear functions comprised of convex curves?

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### Volume of parametric integral of convex set

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### Convex misfit of finite-dimensional convex bodies

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### Relative interior of a normal cone at a face of a convex polytope?

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### Size of a minimal non-negative conic basis

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### Parallelepiped is defined by the volumes of its faces

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### Triangulations of convex surfaces

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### Existence of geodesic convex functions

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### Several convex polytopes in a simplex; fix an extreme point for each; how many can be supported by a function monotonic on all line segments?

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### What is the minimal volume of the intersection of a self-dual cone and the unit ball?

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### Finding a point in the relative interior of the convex hull of a set of integer-valued vectors

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### Relations between conjugate ℓₚ unit ball surface areas

**11**

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### Rigidity of doubled convex caps

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### Projecting two convex polyhedra onto their intersection

**3**

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### Extreme points of a convex set

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### Inner radius of a random convex hull

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### How to show that the origin is not in the convex hull, in this problem?

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### Limiting law of quadratic functions of sample averages

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### Convex hull of the Stiefel manifold with non-negativity constraints

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### What is a natural way to extend a function from a subset of vertices to faces?

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### Enveloping a Jordan curve with a trace of another one

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### “Minkowski Multiplication” of Convex Sets?

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### Is there a dense subset on closed Jordan curve $C$ which its points make intersections under certain rotations?

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### On symmetry and measure concentration rate for convex bodies

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### Homogeneous linear and quadratic inequalities

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### Quantitative error control in Minkowski-Stein formula

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### Numerical approximation of the $\ell_p$ surface area

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### Volume ratio of general $\ell_p$ balls and surfaces

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### On faces of convex sets of positive semidefinite matrices

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### Does a half plane contain intersection of some other half planes? [closed]

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### recursively convex plane curves

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### On the 1/2 assumption on concentration of measure for continuous cube

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### Does Helly's theorem hold in the hyperbolic plane?

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