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Zunwu He

Publications and source records attributed to Zunwu He.

8 recordsLinked to original sources
arXiv2026

Global rigidity of sphere packings in constant curvature background geometry

In this paper, we study the dual characterization of conformal tetrahedra in constant curvature spaces, which develops a geometric technique to obtain the global rigidity of hyperbolic, Euclidean, spherical and ideal hyperbolic sphere packings on a tetrahedron. Moreover, we establish the extended variational principle to obtain the global rigidity of the (ideal) hyperbolic sphere packings on 3-manifolds. We also generalize the conformal tetrahedra to higher dimensions and provide a characterization of conformal $n(\ge3)$-simplices in constant curvature spaces, which is useful for studying higher-dimensional sphere packings.

math.GT↗
arXiv2026

Existence, Rigidity, and Discrete Schwarz--Pick Lemma for Generalized Hyperbolic Circle Packings with Boundary and Discrete Gaussian Curvatures

This paper is concerned with generalized hyperbolic circle packings on compact bordered surfaces, endowed with finite polygonal cellular decompositions. We investigate the problem of realizing generalized hyperbolic circle packings with prescribed geodesic curvatures at boundary vertices, prescribed total geodesic curvatures at interior vertices, and prescribed discrete Gaussian curvatures at the centers of dual circles. We give a necessary and sufficient condition for the existence of such generalized hyperbolic circle packings and show their uniqueness. We also establish a discrete Schwarz--Pick lemma in this setting, including comparison results for vertex curvatures, generalized circle arc lengths, distances, and areas, together with the corresponding rigidity statements.

math.CV↗
arXiv2024

On area-minimizing subgraphs in integer lattices

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 the two-dimensional integer lattice up to isomorphisms, and prove general geometric properties for those in high-dimensional cases.

math.CO↗
arXiv2022

Steklov flows on trees and applications

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 monotonicity and rigidity of the first nonzero Steklov eigenvalues on trees: for finite trees $\g_1$ and $\g_2,$ the first nonzero Steklov eigenvalue of $\g_1$ is greater than or equal to that of $\g_2$, provided that $\g_1$ is a subgraph of $\g_2.$ Moreover, we give the sufficient and necessary condition in which the equality holds.

math.SP↗
arXiv2022

Upper bounds for the Steklov eigenvalues on trees

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 Steklov eigenvalue by the reciprocal of the size of the boundary and the diameter respectively. We also prove similar estimates for higher order Steklov eigenvalues.

math.SP↗
arXiv2020

Remarks on the actions of some groups on the product of Hadamard spaces

For a product of Hadamard spaces $X=X_1\times X_2$ on which some group $G\subset Is(X_1)\times Is(X_2)$ acting, G. Link arXiv:1107.3755v1 introduced the growth rate $δ_θ$ of slope $θ$ to construct a $G-$invariant $(b,θ)$-density. First, we show that $δ_θ$ is continuous in the slope $θ$ as the above group action with some mild condition. Second, we give a negative answer to a question raised by G. Link in \cite{1} in general. And further results about the question are discussed. In the end, we can extent the $(b,θ)$-densities in some reasonable condition.

math.GR↗
arXiv2020

Large quotients of group actions with a contracting element

For any proper action of a non-elementary group $G$ on a proper geodesic metric space, we show that if $G$ contains a contracting element, then there exists a sequence of proper quotient groups whose growth rate tends to the growth rate of $G$. Similar statements are obtained for a product of proper actions with contracting elements. The tools involved in this paper include the extension lemma for the construction of large tree, the theory of rotating families developed by F. Dahmani, V. Guirardel and D. Osin, and the construction of a quasi-tree of metric spaces introduced by M. Bestvina, K. Bromberg and K. Fujiwara. Several applications are given to CAT(0) groups and mapping class groups.

math.GR↗