55 citations · 329 across the 34 of their papers we have counts for
35 papers
Combinatorial Ricci flows on infinite disk triangulations
Huabin Ge, Bobo Hua, Puchun Zhou
In this paper, we introduce combinatorial Ricci flows (CRFs in short) in Euclidean and hyperbolic background geometries on infinite triangulations of the open disk, which are discr…
A combinatorial curvature flow in spherical background geometry
Huabin Ge, Bobo Hua, Puchun Zhou
In [12], the existence of ideal circle patterns in Euclidean or hyperbolic background geometry under the combinatorial conditions was proved using flow approaches. It remains as an…
Combinatorial Ricci flows and the hyperbolization of a class of compact 3-manifolds
Ke Feng, Huabin Ge, Bobo Hua
We prove that for a compact 3-manifold M with boundary admitting an ideal triangulation T with valence at least 10 at all edges, there exists a unique complete hyperbolic metric wi…
Combinatorial Ricci flows with applications to the hyperbolization of cusped 3-manifolds
Ke Feng, Huabin Ge, Bobo Hua
In this paper, we adopt combinatorial Ricci curvature flow methods to study the existence of cusped hyperbolic structure on 3-manifolds with torus boundary. For general pseudo 3-ma…
Circle patterns on surfaces of finite topological type
Huabin Ge, Bobo Hua, Ze Zhou
This paper investigates circle patterns with obtuse exterior intersection angles on surfaces of finite topological type. We characterise the images of the curvature maps and establ…
Partial regularity of harmonic maps from Alexandrov spaces
Huabin Ge, Wenshuai Jiang, Hui-Chun Zhang
In this paper, we prove the Lipschitz regularity of continuous harmonic maps from an finite dimensional Alexandrov space to a compact smooth Riemannian manifold. This solves a conj…
The K"ahler-Ricci flow with Log Canonical Singularities
Albert Chau, Huabin Ge, Ka-Fai Li +1
We establish the existence of the K"ahler-Ricci flow on projective varieties with log canonical singularities. This generalizes some of the existence results of Song-Tian \cite{ST3…
The Dirichlet Problem of Fully Nonlinear Equations on Hermitian Manifolds
Ke Feng, Huabin Ge, Tao Zheng
We study the Dirichlet problem of a class of fully nonlinear elliptic equations on Hermitian manifolds and derive a priori estimates which depend on the initial data on manif…
A note on limit of first eigenfunctions of -Laplacian on graphs
Huabin Ge, Bobo Hua, Wenfeng Jiang
We study the limit of first eigenfunctions of (discrete) -Laplacian on a finite subset of a graph with Dirichlet boundary condition, as We prove that up to a subsequen…
Rigidity of the hexagonal Delaunay triangulated plane
Song Dai, Huabin Ge, Shiguang Ma
We show the rigidity of the hexagonal Delaunay triangulated plane under Luo's PL conformality. As a consequence, we obtain a rigidity theorem for a particular type of locally finit…
Conformal Mesh Parameterization Using Discrete Calabi Flow
Hui Zhao, Xuan Li, Huabin Ge +2
In this paper, we introduce discrete Calabi flow to the graphics research community and present a novel conformal mesh parameterization algorithm. Calabi energy has a succinct and…
3-dimensional Combinatorial Yamabe Flow in Hyperbolic Background Geometry
Huabin Ge, Bobo Hua
We study the 3-dimensional combinatorial Yamabe flow in hyperbolic background geometry. For a triangulation of a 3-manifold, we prove that if the number of tetrahedra incident to e…
On the deformation of ball packings
Huabin Ge, Wenshuai Jiang, Liangming Shen
In this paper, we study the geometric aspects of ball packings on , where is a triangulation on a 3-manifold . We introduce a combinatorial Yamabe…
The Kähler-Ricci flow on pseudoconvex domains
Huabin Ge, Aijin Lin, Liangming Shen
We establish the existence of Kähler-Ricci flow on pseudoconvex domains with general initial metric without curvature bounds. Moreover we prove that this flow is simultaneously com…
A note on Liouville type equations on graphs
Huabin Ge, Bobo Hua, Wenfeng Jiang
In this note, we study the Liouville equation on a graph G satisfying certain isoperimetric inequality. Following the idea of W. Ding, we prove that there exists a unif…
Unified -Flows on Triangulated Manifolds with Two and Three Dimensions
Huabin Ge, Ming Li
In this paper, we introduce a framework of -flows on triangulated manifolds with two and three dimensions, which unifies several discrete curvature flows previously defined…
On the deformation of inversive distance circle packings, III
Huabin Ge, Wenshuai Jiang
Given a triangulated surface , we use Ge-Xu's -flow \cite{Ge-Xu1} to deform any initial inversive distance circle packing metric to a metric with constant -curvature. More…
The -Yamabe equation on graph
Huabin Ge, Wenfeng Jiang
We study the following -Yamabe equation on a connected finite graph where is the discrete -Laplacian, and $g,…
Kazdan-Warner equation on infinite graphs
Huabin Ge, Wenfeng Jiang
We concern in this paper the graph Kazdan-Warner equation \begin{equation*} Δf=g-he^f \end{equation*} on an infinite graph, the prototype of which comes from the smooth Kazdan-Warn…
On a combinatorial curvature for surfaces with inversive distance circle packing metrics
Huabin Ge, Xu Xu
In this paper, we introduce a new combinatorial curvature on triangulated surfaces with inversive distance circle packing metrics. Then we prove that this combinatorial curvature h…
Kazdan-Warner equation on graph in the negative case
Huabin Ge
Let be a connected finite graph. In this short paper, we reinvestigate the Kazdan-Warner equation with on , where defined on is a known fun…
A p-th Yamabe equations on graph
Huabin Ge
Assume . Consider the following -th Yamabe equation on a connected finite graph : where is the discrete -Laplacian, and $…
p-th Kazdan-Warner equation on graph
Huabin Ge
Let be a connected finite graph and be the set of functions defined on . Let be the discrete -Laplacian on with and , where $k\in C(…
Liouville-type theorems on the complete gradient shrinking Ricci solitons
Huabin Ge, Shijin Zhang
We prove that there does not exist non-constant positive -harmonic function on the complete gradient shrinking Ricci solitons. We also prove the $L^{p}(p\geq 1 \ {\rm or}\ 0<p\l…