Question

Every symmetric convex body in $\mathbb{R}^n$ is the closed unit ball of a norm on $\mathbb{R}^n$ - why?

score 1k · Answer 1 · 2020-12-28 12:17:13

1k

Views

Every symmetric convex body in $\mathbb{R}^n$ is the closed unit ball of a norm on $\mathbb{R}^n$ - why?

Published on 28 Dec 2020 - 12:17

score 74 · Answer 2 · 2026-03-28 23:19:37

74

Views

Why does the cube have the fewest facets among (centrally) symmetric polytopes in $\mathbb{R}^n$?

Published on 28 Mar 2026 - 23:19

score 410 · Answer 3 · 2020-12-31 04:43:27

410

Views

Understanding the notion of distance between two symmetric convex bodies

Published on 31 Dec 2020 - 4:43

score 264 · Answer 4 · 2026-03-27 10:07:13

264

Views

Convex hull properties

Published on 27 Mar 2026 - 10:07

score 100 · Answer 5 · 2021-01-02 16:54:50

100

Views

Reformulation of a theorem about the lower bound on no. of facets of a symmetric polytope in $\mathbb{R}^n$

Published on 02 Jan 2021 - 16:54

score 68 · Answer 6 · 2021-01-03 09:06:41

68

Views

How many faces does an $n$-dimensional slice of $[-1,1]^m$ have?

Published on 03 Jan 2021 - 9:06

score 49 · Answer 7 · 2021-01-03 10:46:35

49

Views

To show the equivalence of two statements related to $B^n_2 \subset K \subset dB^n_2$

Published on 03 Jan 2021 - 10:46

score 147 · Answer 8 · 2026-03-27 21:20:35

147

Views

What inequalities for convex sets are known since the work of Scott and Awyong?

Published on 27 Mar 2026 - 21:20

score 290 · Answer 9 · 2026-02-23 15:13:24

290

Views

How to recover a closed convex set from its support function?

Published on 23 Feb 2026 - 15:13

score 31 · Answer 10 · 2021-01-04 05:50:02

31

Views

Interconverting different equations for spherical caps in $\mathbb{R}^n$

Published on 04 Jan 2021 - 5:50

score 112 · Answer 11 · 2021-01-05 19:22:29

112

Views

Triangle lower bound of a convex function

Published on 05 Jan 2021 - 19:22

score 376 · Answer 12 · 2026-03-25 20:35:12

376

Views

Intersection of a pointed cone and a hyperplane is a polytope?

Published on 25 Mar 2026 - 20:35

score 161 · Answer 13 · 2021-01-08 11:31:33

161

Views

Prove certain set is convex

Published on 08 Jan 2021 - 11:31

score 67 · Answer 14 · 2026-03-27 07:13:30

67

Views

Find convex closure of certain set

Published on 27 Mar 2026 - 7:13

score 939 · Answer 15 · 2021-01-10 06:55:51

939

Views

Strong convexity and the composition of convex functions

Published on 10 Jan 2021 - 6:55

List Question

Every symmetric convex body in $\mathbb{R}^n$ is the closed unit ball of a norm on $\mathbb{R}^n$ - why?

Why does the cube have the fewest facets among (centrally) symmetric polytopes in $\mathbb{R}^n$?

Understanding the notion of distance between two symmetric convex bodies

Convex hull properties

Reformulation of a theorem about the lower bound on no. of facets of a symmetric polytope in $\mathbb{R}^n$

How many faces does an $n$-dimensional slice of $[-1,1]^m$ have?

To show the equivalence of two statements related to $B^n_2 \subset K \subset dB^n_2$

What inequalities for convex sets are known since the work of Scott and Awyong?

How to recover a closed convex set from its support function?

Interconverting different equations for spherical caps in $\mathbb{R}^n$

Triangle lower bound of a convex function

Intersection of a pointed cone and a hyperplane is a polytope?

Prove certain set is convex

Find convex closure of certain set

Strong convexity and the composition of convex functions

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