MSC2020 · 52Axx

General convexity

12 mapped entries · Browse and filter all →

Counts include all statuses and descendants. Classifications are editorial or inferred from community fields, not an AMS assessment of the problem.

Subcategories

52A01Axiomatic and generalized convexity0 52A05Convex sets without dimension restrictions (aspects of convex geometry)0 52A07Convex sets in topological vector spaces (aspects of convex geometry)0 52A10Convex sets in

2

dimensions (including convex curves)0 52A15Convex sets in

3

dimensions (including convex surfaces)0 52A20Convex sets in

n

dimensions (including convex hypersurfaces)2 52A21Convexity and finite-dimensional Banach spaces (including special norms, zonoids, etc.) (aspects of convex geometry)0 52A22Random convex sets and integral geometry (aspects of convex geometry)0 52A23Asymptotic theory of convex bodies4 52A27Approximation by convex sets0 52A30Variants of convex sets (star-shaped, (

m, n

)-convex, etc.)0 52A35Helly-type theorems and geometric transversal theory0 52A37Other problems of combinatorial convexity0 52A38Length, area, volume and convex sets (aspects of convex geometry)0 52A39Mixed volumes and related topics in convex geometry0 52A40Inequalities and extremum problems involving convexity in convex geometry7 52A41Convex functions and convex programs in convex geometry0 52A55Spherical and hyperbolic convexity0 52A99General convexity0

Mapped problems

OP-12149Geometry and topologyStatus unassessed

Heilbronn problem in an arbitrary convex bounding box (AlphaEvolve problem 49)

Heilbronn problem in an arbitrary convex bounding box (AlphaEvolve problem 49). Current research status is unassessed; the repository records AlphaEvolve’s result on this question.

AlphaEvolve Repository of Problems — Georgiev, Gómez-Serrano, Tao & Wagner· Licensed source statement· 2025

OP-12148Geometry and topologyStatus unassessed

Heilbronn problem in a fixed bounding box (AlphaEvolve problem 48)

Heilbronn problem in a fixed bounding box (AlphaEvolve problem 48). Current research status is unassessed; the repository records AlphaEvolve’s result on this question.

AlphaEvolve Repository of Problems — Georgiev, Gómez-Serrano, Tao & Wagner· Licensed source statement· 2025

OP-12141Geometry and topologyStatus unassessed

Points on sphere maximizing the volume (AlphaEvolve problem 41)

Points on sphere maximizing the volume (AlphaEvolve problem 41). Current research status is unassessed; the repository records AlphaEvolve’s result on this question.

AlphaEvolve Repository of Problems — Georgiev, Gómez-Serrano, Tao & Wagner· Licensed source statement· 2025

OP-12085Geometry and topologyOpen

Reverse Brunn-Minkowski constant ( $C_{70}$ )

Reverse Brunn-Minkowski constant: determine C 70 or improve its bounds; the repository records 1 (lower) and < infty (upper).

Optimization Constants in Mathematics — Davis, Ivanisvili & Tao· Licensed source statement· 2026

OP-12049Geometry and topologyOpen

Hadwiger covering / illumination number in $\mathbb{R}^3$ ( $C_{39}$ )

Hadwiger covering / illumination number in mathbb R ^3 : determine C 39 or improve its bounds; the repository records 8 (lower) and 14 (upper).

Optimization Constants in Mathematics — Davis, Ivanisvili & Tao· Licensed source statement· 2026

OP-12038Geometry and topologyOpen

Smallest dimension in which Borsuk’s conjecture fails ( $C_{28}$ )

Smallest dimension in which Borsuk’s conjecture fails: determine C 28 or improve its bounds; the repository records 4 (lower) and 63 (upper).

Optimization Constants in Mathematics — Davis, Ivanisvili & Tao· Licensed source statement· 2026

OP-12033Geometry and topologyOpen

Mahler volume product constant ( $C_{25}$ )

Mahler volume product constant: determine C 25 or improve its bounds; the repository records pi (lower) and 4 (upper).

Optimization Constants in Mathematics — Davis, Ivanisvili & Tao· Licensed source statement· 2026

OP-12025ProbabilityOpen

KLS constant for log-concave probability measures ( $C_{20c}$ )

KLS constant for log-concave probability measures: determine C 20c or improve its bounds; the repository records sqrt pi/2 approx 1.25331 (lower) and infty (upper).

Optimization Constants in Mathematics — Davis, Ivanisvili & Tao· Licensed source statement· 2026

OP-12024Geometry and topologyOpen

Isotropic constant of a log-concave probability measure ( $C_{20b}$ )

Isotropic constant of a log-concave probability measure: determine C 20b or improve its bounds; the repository records 1/e (lower) and < infty (upper).

Optimization Constants in Mathematics — Davis, Ivanisvili & Tao· Licensed source statement· 2026

OP-12023ProbabilityOpen