## New answers tagged convex-geometry

1
vote

### Cone unfolding of space curves

Pardon me for this bit of self-promotion, especially because this is
only tangential to the OP's concerns.
But cone unrolling and Anton Petrunin's mention of Alexandrov's developments, in conjunction ...

- 146k

1
vote

### Cone unfolding of space curves

Liberman used cylinder unfolding to study geodesics on convex surfaces.
[Либерман, И. М. «Геодезические линии на выпуклых поверхностях». ДАН СССР. 32.2. (1941), 310—313.]
Right now standard ...

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0
votes

### Do subgradient inequalities hold for matrix convex functions?

Some further research has pointed out the answer as affirmative (though I will leave the question unanswered for now, as I'm still perplexed by Ando's rank restriction, which now seems unnecessary).
...

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5
votes

### In a set of n points on $R^d$, each point can be "well separated" from the rest by a linear functional. Is the dimension necessarily $\Omega(n)$?

Take all the vectors of the form $e_i+e_j$, $i\neq j$, where $e_1,\dots,e_d$ is a base in $\mathbb R^d$. They satisfy your requirements, the vector $e_i+e_j$ being separated from the others by $e_i^*+...

- 19.8k

6
votes

### Status of Barany's conjecture?

2022 update
Bárány's conjecture seems to have been answered in the affirmative by Joshua Hinman in a rather short paper of only 8 pages:
Joshua Hinman. "A Positive Answer to Bárány's Question on ...

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