31 citations · 80 across the 22 of their papers we have counts for
23 papers
Rigidity of the Delaunay triangulations of the plane
Song Dai, Tianqi Wu
We proved a rigidity result for Delaunay triangulations of the plane under Luo's discrete conformal change, extending previous results on hexagonal triangulations. Our result is a…
Prescribed curvature problem for discrete conformality on convex spherical cone-metrics
Ivan Izmestiev, Roman Prosanov, Tianqi Wu
Let be the 2-sphere and be a finite set of at least three points. We show that for each function satisfying elementary necessary condit…
A sharp leading order asymptotic of the diameter of a long range percolation graph
Tianqi Wu
Many real-world networks exhibit the so-called small-world phenomenon: their typical distances are much smaller than their sizes. One mathematical model for this phenomenon is a lo…
Rigidity of Acute Triangulations of the Plane
Tianqi Wu
We show that a uniformly acute triangulation of the plane is rigid under Luo's discrete conformal change, extending previous results on hexagonal triangulations. Our result is a di…
Surface Eigenvalues with Lattice-Based Approximation In comparison with analytical solution
Yingying Wu, Tianqi Wu, Shing-Tung Yau
In this paper, we propose a meshless method of computing eigenvalues and eigenfunctions of a given surface embedded in . We use point cloud data as input and generate…
The Deformation Space of Delaunay Triangulations of the Sphere
Yanwen Luo, Tianqi Wu, Xiaoping Zhu
In this paper, we determine the topology of the spaces of convex polyhedra inscribed in the unit -sphere and the spaces of strictly Delaunay geodesic triangulations of the unit…
The Convergence of Discrete Uniformizations for Genus Zero Surfaces
Yanwen Luo, Tianqi Wu, Xiaoping Zhu
The notion of discrete conformality proposed by Luo and Bobenko-Pinkall-Springborn on triangle meshes has rich mathematical theories and wide applications. Gu et al. proved that th…
Fractional combinatorial Calabi flow on surfaces
Tianqi Wu, Xu Xu
Using the fractional discrete Laplace operator for triangle meshes, we introduce a fractional combinatorial Calabi flow for discrete conformal structures on surfaces, which unifies…
The Deformation Spaces of Geodesic Triangulations of Flat Tori
Yanwen Luo, Tianqi Wu, Xiaoping Zhu
We prove that the deformation space of geodesic triangulations of a flat torus is homotopy equivalent to a torus. This solves an open problem proposed by Connelly et al. in 1983, i…
The Deformation Space of Geodesic Triangulations and Generalized Tutte's Embedding Theorem
Yanwen Luo, Tianqi Wu, Xiaoping Zhu
We proved the contractibility of the deformation space of the geodesic triangulations on a closed surface of negative curvature. This solves an open problem proposed by Connelly et…
Discrete Conformal Geometry of Polyhedral Surfaces and Its Convergence
Feng Luo, Jian Sun, Tianqi Wu
The paper proves a result on the convergence of discrete conformal maps to the Riemann mappings for Jordan domains. It is a counterpart of Rodin-Sullivan's theorem on convergence o…
Computing Harmonic Maps and Conformal Maps on Point Clouds
Tianqi Wu, Shing-Tung Yau
We propose a novel meshless method to compute harmonic maps and conformal maps for surfaces embedded in the Euclidean 3-space, using point cloud data only. Given a surface, or a po…
The Convergence of Discrete Uniformizations for Closed Surfaces
Tianqi Wu, Xiaoping Zhu
The notions of discrete conformality on triangle meshes have rich mathematical theories and wide applications. The related notions of discrete uniformizations on triangle meshes, s…
Koebe conjecture and the Weyl problem for convex surfaces in hyperbolic 3-space
Feng Luo, Tianqi Wu
We prove that the Koebe circle domain conjecture is equivalent to the Weyl type problem that every complete hyperbolic surface of genus zero is isometric to the boundary of the hyp…
Ergodicity of the infinite swapping algorithm at low temperature
Georg Menz, André Schlichting, Wenpin Tang +1
Sampling Gibbs measures at low temperatures is an important task but computationally challenging. Numerical evidence suggests that the infinite-swapping algorithm (isa) is a promis…
A One-Sentence Inverse Image Proof of Lusin's Theorem
Samuel J. Ferguson, Tianqi Wu
Standard proofs of Lusin's theorem, using simple functions, are sometimes quite elaborate. Here, we give a one-sentence proof of Lusin's theorem. We do not believe our approach, by…
Toward a quantitative theory of the hydrodynamic limit
Deniz Dizdar, Georg Menz, Felix Otto +1
This article provides non-trivial technical ingredients for the article "The quantitative hydrodynamic limit of the Kawasaki dynamics" by the same authors. In that work a quantitat…
The quantitative hydrodynamic limit of the Kawasaki dynamics
Deniz Dizdar, Georg Menz, Felix Otto +1
We derive for the first time in the literature a rate of convergence in the hydrodynamic limit of the Kawasaki dynamics for a one-dimensional lattice system. We use an adaptation o…
Discrete Conformal Deformation: Algorithm and Experiments
Jian Sun, Tianqi Wu, Xianfeng Gu +1
In this paper, we introduce a definition of discrete conformality for triangulated surfaces with flat cone metrics and describe an algorithm for solving the problem of prescribing…
Partition Statistics Equidistributed with the Number of Hook Difference One Cells
Jiaoyang Huang, Andrew Senger, Peter Wear +1
Let be a partition, viewed as a Young diagram. We define the hook difference of a cell of to be the difference of its leg and arm lengths. Define to be the num…
A discrete uniformization theorem for polyhedral surfaces II
Xianfeng Gu, Ren Guo, Feng Luo +2
A discrete conformality for hyperbolic polyhedral surfaces is introduced in this paper. This discrete conformality is shown to be computable. It is proved that each hyperbolic poly…
A discrete uniformization theorem for polyhedral surfaces
Xianfeng Gu, Feng Luo, Jian Sun +1
A discrete conformality for polyhedral metrics on surfaces is introduced in this paper which generalizes earlier work on the subject. It is shown that each polyhedral metric on a s…
Rigidity of Infinite Hexagonal Triangulation of the Plane
Tianqi Wu, Xianfeng Gu, Jian Sun
In the paper, we consider the rigidity problem of the infinite hexagonal triangulation of the plane under the piecewise linear conformal changes introduced by Luo in [5]. Our resul…