Bisectors in the Heisenberg group I
We show that metric bisectors with respect to the Korányi metric in the Heisenberg group are spinal spheres and vice versa. We also calculate explicitly their horizontal mean curvature.
math.DG↗
arXiv subjects
Gaoshun Gou
Publications and source records attributed to Gaoshun Gou.
The modulus of the Korányi ellipsoidal ring
The Korányi ellipsoidal ring $\mathcal{E}$ of radii $B$ and $A$, $0<B<A$, is defined as the image of the Korányi spherical ring of the same radii and centred at the origin via a linear contact map $L$ in the Heisenberg group. If $K\ge 1$ is the maximal distortion of $L$ then we prove that the modulus of $\mathcal{E}$ is equal to $$ {\rm mod}(\mathcal{E})=\left(\frac{3}{8}\Big(K^2+\frac{1}{K^2}\Big)+\frac{1}{4}\right)\frac{π^2}{(\log (A/B))^3}. $$
math.DG↗
The Moduli Space of Points in the Boundary of Quaternionic Hyperbolic Space
Let $\mathcal{F}_1(n,m)$ be the space of ordered m-tuples of pairwise distinct points in $\partial \mathbf{H}_{\mathbb{H}}^n$ up to its isometry group $PSp(n,1)$. It is a real $2m^2-6m+5-\sum^{m-n-1}_{i=1}{m-2 \choose n-1+i}$ dimensional algebraic variety when $m>n+1$. In this paper, we construct and describe the moduli space of $\mathcal{F}_1(n,m)$, in terms of the Cartan's angle and cross-ratio invariants, by applying the Moore's determinant.
math.CV↗