8 papers
Conformal tetrahedra and global rigidity of sphere packings in constant curvature background geometry
Zunwu He, Guangming Hu, Ziping Lei
In this paper, we give the dual characterization of conformal tetrahedra in constant curvature spaces, which develops a geometric technique to obtain the global rigidity of (ideal)…
Existence, Rigidity, and Discrete Schwarz--Pick Lemma for Generalized Hyperbolic Circle Packings with Boundary and Discrete Gaussian Curvatures
Yu Sun, Lei Bao, Wenhao Fu +1
This paper is concerned with generalized hyperbolic circle packings on compact bordered surfaces, endowed with finite polygonal cellular decompositions. We investigate the problem…
On area-minimizing subgraphs in integer lattices
Zunwu He, Bobo Hua
We introduce area-minimizing subgraphs in an infinite graph via the formulation of functions of bounded variations initiated by De Giorgi. We classify area-minimizing subgraphs in…
Steklov flows on trees and applications
Zunwu He, Bobo Hua
We introduce the Steklov flows on finite trees, i.e. the flows (or currents) associated with the Steklov problem. By constructing appropriate Steklov flows, we prove the monotonici…
Upper bounds for the Steklov eigenvalues on trees
Zunwu He, Bobo Hua
In this paper, we study the upper bounds for discrete Steklov eigenvalues on trees via geometric quantities. For a finite tree, we prove sharp upper bounds for the first nonzero St…
Harmonic functions of polynomial growth on infinite penny graphs
Zunwu He, Bobo Hua
For an infinite penny graph, we study the finite-dimensional property for the space of harmonic functions, or ancient solutions of the heat equation, of polynomial growth. We prove…
Remarks on the actions of some groups on the product of Hadamard spaces
Zunwu He
For a product of Hadamard spaces on which some group acting, G. Link arXiv:1107.3755v1 introduced the growth rate of slope…
Large quotients of group actions with a contracting element
Zunwu He, Jinsong Liu, Wenyuan Yang
For any proper action of a non-elementary group on a proper geodesic metric space, we show that if contains a contracting element, then there exists a sequence of proper qu…