scispace - formally typeset
Search or ask a question
Author

Wensheng Cao

Bio: Wensheng Cao is an academic researcher from Wuyi University. The author has contributed to research in topics: Ricci-flat manifold & Relatively hyperbolic group. The author has an hindex of 1, co-authored 1 publications receiving 3 citations.

Papers
More filters
Journal ArticleDOI
Wensheng Cao1
TL;DR: In this paper, a lower bound for the radius of the largest inscribed ball in quaternionic hyperbolic n-manifolds was obtained by using the Zassenhaus neighborhood of Sp(n, 1).
Abstract: By use of the Zassenhaus neighborhood of Sp(n,1), we obtain an explicit lower bound for the radius of the largest inscribed ball in quaternionic hyperbolic n-manifold $\mathscr{M} = \mathbf H_\mathbf H ^n/Γ$. As an application, we obtain a lower bound for the volumes of quaternionic hyperbolic n-manifolds.

4 citations


Cited by
More filters
Dissertation
15 Dec 2016
TL;DR: In this paper, a reseau remarquable des isometries du plan hyperbolique quaternionique, le groupe modulaire d’Hurwitz, is presented.
Abstract: Dans une premiere partie de cette these, nous donnons des minorations universelles ne dependant que de la dimension – explicites, de trois invariants globaux des quotients des espaces hyperboliques quaternioniques : leur rayon maximal, leur volume, ainsi que leur caracteristique d’Euler. Nous donnons egalement une majoration de leur constante de Margulis, montrant que celle-ci decroit au moins comme une puissance negative de la dimension. Dans une seconde partie, nous etudions un reseau remarquable des isometries du plan hyperbolique quaternionique, le groupe modulaire d’Hurwitz. Nous montrons en particulier qu’il est engendre par quatres elements, et construisons un domaine fondamental pour le sous-groupe des isometries de ce reseau qui stabilisent un point a l’infini.

6 citations

Posted Content
TL;DR: In this paper, the authors combine H. C. Wang's radius estimate with an improved upper sectional curvature bound for a canonical left-invariant metric on a real semisimple Lie group and use Gunther's volume comparison theorem to deduce an explicit uniform lower volume bound for arbitrary orbifold quotients of a given irreducible symmetric spaces of non-compact type.
Abstract: A classic theorem of Kazhdan and Margulis states that for any semisimple Lie group without compact factors, there is a positive lower bound on the covolume of lattices. H. C. Wang's subsequent quantitative analysis showed that the fundamental domain of any lattice contains a ball whose radius depends only on the group itself. A direct consequence is a positive minimum volume for orbifolds modeled on the corresponding symmetric space. However, sharp bounds are known only for hyperbolic orbifolds of dimensions two and three, and recently for quaternionic hyperbolic orbifolds of all dimensions. As in arXiv:0911.4712 and arXiv:1205.2011, this article combines H. C. Wang's radius estimate with an improved upper sectional curvature bound for a canonical left-invariant metric on a real semisimple Lie group and uses Gunther's volume comparison theorem to deduce an explicit uniform lower volume bound for arbitrary orbifold quotients of a given irreducible symmetric spaces of non-compact type. The numerical bound for the octonionic hyperbolic plane is the first such bound to be given. For (real) hyperbolic orbifolds of dimension greater than three, the bounds are an improvement over what was previously known.

2 citations

Journal ArticleDOI
Wensheng Cao1, Jianli Fu1
TL;DR: In this paper, a lower bound for the volume of a quaternionic hyperbolic orbifold that depends only on dimension was derived by using H. C. Wang's bound on the radius of a ball embedded in the fundamental domain of a lattice of a semisimple Lie group.
Abstract: By use of H. C. Wang’s bound on the radius of a ball embedded in the fundamental domain of a lattice of a semisimple Lie group, we construct an explicit lower bound for the volume of a quaternionic hyperbolic orbifold that depends only on dimension.

1 citations

21 Jun 2023
TL;DR: In this paper , it was shown that each matrix in U(1,1;\mathbb{H}) which corresponds to an elliptic quaternionic M\"{o}bius transformation (g_T(z) = 0.
Abstract: Denote by $\mathbb{H}$ the set of all quaternions. We are interested in the group $U(1,1;\mathbb{H})$, which is a subgroup of $2\times 2$ quaternionic matrix group and is sometimes called $Sp(1,1)$. As well known, $U(1,1;\mathbb{H})$ corresponds to the quaternionic M\"{o}bius transformations on the unit ball in $\mathbb{H}$. In this article, some similar invariants on $U(1,1;\mathbb{H})$ are discussed. Our main result shows that each matrix $T\in U(1,1;\mathbb{H})$, which corresponds to an elliptic quaternionic M\"{o}bius transformation $g_T(z)$, could be $U(1,1;\mathbb{H})$-similar to a diagonal matrix.