# Tag Info

Accepted

### Length and curvature for closed curves in negatively curved spaces

The Reshetnyak majorization theorem (see 9.56) states that any closed rectifiable curve $\alpha$ in a CAT(0) length space $U$ can be majorized by a convex plane figure $F$; that is, there is short (= ...
• 39.3k

### Packing twelve spherical caps to maximize tangencies

As an extension of the problem (which turns out to have some physical significance), we may consider what would happen if we were to allow the twelve vectors to "land" within the unit ball ...
• 619
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 ...
• 39.3k
1 vote

### 4D Duoprisms based on nonconvex polygons

The great duoantiprism can be constructed using a compound of two pentagonal-pentagrammic duoprisms by inserting additional edges, or by alternating a decagonal-decagrammic duoprism.
• 2,166

### Which pyramids fill space?

About the tetrahedra problem, I have found this reference/proof that they cannot be used to fill 3D space (since the proven upper bound is smaller than $100 \cdot (1-2.7 \cdot 10^{-25})\%$: https://en....
• 301
Accepted

### Finitely generated groups with Hölder-exotic space of ends?

The question is solved positively in the paper The Hausdorff dimension of the harmonic measure for relatively hyperbolic groups by Matthieu Dussaule, Wenyuan Yang, which appeared on arXiv on October ...
Accepted

### Intersection of conical neighbourhoods on a polyhedral space

You say "The same is true for a tubular neighborhood of the edge". This is not correct, but it is true if you stay away from the endpoints. So $U$ should be defined as a tubular neighborhood ...
• 39.3k