Lizhao Zhang

activity

20072023

most citedRigidity and volume preserving deformation on degenerate simplices

4 citations · 4 across the 5 of their papers we have counts for

collaborators

5 papers

math.MG2023

Simplices with fixed volumes of codimension 2 faces in a continuous deformation

Lizhao Zhang

For any $n$ -dimensional simplex in the Euclidean space $R^{n}$ with $n \geq 4$ , it is asked that if a continuous deformation preserves the volumes of all the codimension 2 fac…

math.MG2023

A volume correspondence between anti-de Sitter space and its boundary

Lizhao Zhang

Let $H_{1}^{n + 1}$ be the $(n + 1)$ -dimensional anti-de Sitter space (AdS), in this paper we propose to extend $H_{1}^{n + 1}$ conformally to another copy of $\mathbb{H}^{…

math.MG2018

Lifting degenerate simplices with a single volume constraint

Lizhao Zhang

Let $M^{d}$ be the spherical, Euclidean, or hyperbolic space of dimension $d \geq n + 1$ . Given any degenerate $(n + 1)$ -simplex $A$ in $M^{d}$ with non-degenerate $n$ -faces $F_{i}$ ,…

math.MG2018

On the total volume of the double hyperbolic space

Lizhao Zhang

Let the \emph{double hyperbolic space} $DH^{n}$ , proposed in this paper as an extension of the hyperbolic space $H^{n}$ , contain a two-sheeted hyperboloid with the tw…

math.MG2007★ 4 cited

Rigidity and volume preserving deformation on degenerate simplices

Lizhao Zhang

Given a degenerate $(n + 1)$ -simplex in a $d$ -dimensional space $M^{d}$ (Euclidean, spherical or hyperbolic space, and $d \geq n$ ), for each $k$ , $1 \leq k \leq n$ , Radon's theorem induce…