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4 votes
1 answer
183 views

What are some properties of the leading eigenvalue of a product of inversions in mutually tangent spheres?

Let $S_1, \ldots, S_n$ be a collection of $n \geq 4$ pairwise tangent hyperspheres in $\mathbb{R}^{n-2}$ with disjoint interiors, and $\iota_i$ be the inversion in $S_i$. Viewing the conformal group ...
Sami Douba's user avatar
11 votes
1 answer
258 views

Algorithmic Borel finiteness for hyperbolic manifolds

It is a theorem of Borel that there is a finite number of arithmetic hyperbolic manifolds of volume bounded above by $V.$ Is there any algorithm (or hope of an algorithm) to actually construct all of ...
Igor Rivin's user avatar
  • 96.4k
7 votes
0 answers
172 views

Subgroups of $\mathbb{Z}^{n}$ with rotational symmetries

Schmidt (https://projecteuclid.org/euclid.dmj/1077377618) showed that the number of $m$-dimensional subgroups of $\mathbb{Z}^{n}$ of covolume $\leq X$ is $$c_{1}\left(m,n\right)X^{n}+O\left(X^{n-\...
Tal H's user avatar
  • 273