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Results tagged with hyperbolic-geometry
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user 20595
7
votes
2
answers
440
views
Are there infinitely many commensurable classes of finite-covolume hyperbolic Coxeter groups?
Allcock(2006) proved that
there are infinitely many finite-covolume (resp. cocompact) Coxeter groups acting on hyperbolic space $H^n$ for every $n\le 19$ (resp. $n\le 6$).
His main technique of …
- 2,581
7
votes
1
answer
341
views
For a 3D Apollonian packing, do we really know that the Hausdorff dimension of the complemen...
The fractal dimension of the 3D Apollonian packing is computed in this paper.
In the introduction, the authors cite three of Boyd's paper (Ref 2, 5, 6) to support that the fractal dimension (Hausdo …
- 2,581
1
vote
Accepted
For a 3D Apollonian packing, do we really know that the Hausdorff dimension of the complemen...
OK, I found the reference:
For those who care, it's recently proved in a much stronger form by Oh and Shah in The asymptotic distribution of circles in the orbits of Kleinian groups. The paper is ab …
- 2,581