List questions from convex-geometry

Published on 27 Mar 2026 - 7:14

26

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Planar convex sets whose self-intersections are similar to themselves

Published on 25 Mar 2026 - 15:58

20

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Intersection of Symmetric Convex Sets

Published on 30 Mar 2026 - 13:52

75

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Prove the set ext(S)$=\{x\in\mathbb{R}^n:x_i^2=1,i=1\ldots n\}$ where $S=\{x\in\mathbb{R}^n:||x||_{\infty}\leq 1\}$

Published on 10 Nov 2020 - 9:28

89

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Given upper bound of the width, which closed convex curve has the largest area?

Published on 11 Nov 2020 - 15:47

57

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Given a convex set $S\subset\mathbb{R}^2$ of unit area, how small of a quadrilateral can we inscribe it in?

Published on 12 Nov 2020 - 20:32

334

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Example of convex sets

Published on 13 Nov 2020 - 17:54

173

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Simple Triangle-like Inequality for a general norm

Published on 23 Feb 2026 - 16:55

260

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Translated convex sets proof

Published on 13 Nov 2020 - 18:43

36

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What polytope is obtained on the midway cut of a simplex?

Published on 29 Mar 2026 - 2:47

36

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Among 3D convex bodies of unit width, which one has minimal volume?

Published on 19 Nov 2020 - 21:04

186

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Intersection of a Convex Polyhedron and a Plane

Published on 20 Nov 2020 - 13:54

33

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Suppose $F(x+y) \geq \frac{x}{x+y} F(x) + \frac{y}{x+y}F(y)$ for all $x ,y \in \mathbb{R}_+$. Is $F$ convex?

Published on 20 Nov 2020 - 21:35

64

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converting con-convex region to convex

Published on 29 Mar 2026 - 15:14

61

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For which $c\in \mathbb R$ the function $\kappa(t) := ct^4(1-t)^4$ can be curvature of regular, closed, convex curve

Published on 21 Nov 2020 - 6:47

List Question

How can Radon's lemma be useful?

Planar convex sets whose self-intersections are similar to themselves

Intersection of Symmetric Convex Sets

Prove the set ext(S)$=\{x\in\mathbb{R}^n:x_i^2=1,i=1\ldots n\}$ where $S=\{x\in\mathbb{R}^n:||x||_{\infty}\leq 1\}$

Given upper bound of the width, which closed convex curve has the largest area?

Given a convex set $S\subset\mathbb{R}^2$ of unit area, how small of a quadrilateral can we inscribe it in?

Example of convex sets

Simple Triangle-like Inequality for a general norm

Translated convex sets proof

What polytope is obtained on the midway cut of a simplex?

Among 3D convex bodies of unit width, which one has minimal volume?

Intersection of a Convex Polyhedron and a Plane

Suppose $F(x+y) \geq \frac{x}{x+y} F(x) + \frac{y}{x+y}F(y)$ for all $x ,y \in \mathbb{R}_+$. Is $F$ convex?

converting con-convex region to convex

For which $c\in \mathbb R$ the function $\kappa(t) := ct^4(1-t)^4$ can be curvature of regular, closed, convex curve

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