6 citations · 12 across the 15 of their papers we have counts for
17 papers
Discrete uniformization of polyhedral surfaces
Feng Luo, Yanwen Luo, Zhenghao Rao +1
The main result of the paper shows that each connected polyhedral surface with a hyperbolic background metric, or a Euclidean background metric with uniformly bounded circumdisk ra…
Morphing Graphs on Hyperbolic Surfaces
Yanwen Luo, Yuan Luo
We propose the first algorithm to morph geometric graphs on hyperbolic surfaces. It is based on a generalization of Tutte's spring embedding theorem on essentially 3-vertex-connect…
A Rigidity Theorem for Convex Sets in Hyperbolic 3-Space
Feng Luo, Yanwen Luo, Zhenghao Rao
Pogorelov's rigidity theorem states that a compact convex body in the hyperbolic 3-space is determined up to isometry by the intrinsic path metric on its boundary. The main result…
Infinite rigidity of inversive distance circle packings in the Poincaré disk
Yanwen Luo, Xu Xu, Chao Zheng
The maximum principle for hyperbolic inversive distance circle packings on polyhedral surfaces is established,which unifies and generalizes existing maximum principles for various…
Rigidity of infinite inversive distance circle packings in the plane
Yanwen Luo, Xu Xu, Siqi Zhang
In 2004, Bowers-Stephenson [2] introduced the inversive distance circle packings as a natural generalization of Thurston's circle packings. They further conjectured the rigidity of…
Maximal principles in discrete conformal geometry with application to the rigidity of infinite triangulations
Yanwen Luo, Xu Xu, Chao Zheng
In this paper, maximum principles for Euclidean and hyperbolic discrete conformal structures on polyhedral surfaces are established. These maximum principles unify and generalize t…
A note on graph drawings with star-shaped boundaries in the plane
Yanwen Luo
In this note, we propose a straightforward method to produce an straight-line embedding of a planar graph where one face of a graph is fixed in the plane as a star-shaped polygon.…
Spaces of Geodesic Triangulations Are Cells
Yanwen Luo, Zhenghao Rao, Tianqi Wu +1
It has been shown that spaces of geodesic triangulations of closed negatively curved surfaces are contractible. Here we prove that these spaces are homeomorphic to Euclidean spaces…
The convergence of inversive distance circle packings to the Riemann mapping
Yuxiang Chen, Yanwen Luo, Xu Xu
Bowers and Stephenson introduced the notion of inversive distance circle packings as a natural generalization of Thurston's circle packings. They further conjectured that discrete…
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…
Combinatorial Calabi flows on surfaces with boundary
Yanwen Luo, Xu Xu
Motivated by Luo's combinatorial Yamabe flow on closed surfaces \cite{L1} and Guo's combinatorial Yamabe flow on surfaces with boundary \cite{Guo}, we introduce combinatorial Calab…
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…
Spaces of Geodesic Triangulations of Surfaces
Yanwen Luo
We give a short proof of the contractibility of the space of geodesic triangulations with fixed combinatorial type of a convex polygon in the Euclidean plane. Moreover, for any $n>…
Comparing shapes of high genus surfaces
Yanwen Luo
In this paper, we define a new metric structure on the shape space of a high genus surface. We introduce a rigorous definition of a shape of a surface and construct a metric based…
Diffeomorphism Invariance of Geometric Descriptions of Palatini and Ashtekar Gravity
Yan Luo, Ming-Xue Shao, Zhong-Yuan Zhu
In this paper, we explicitly prove the presymplectic forms of the Palatini and Ashtekar gravity to be zero along gauge orbits of the Lorentz and diffeomorphism groups, which ensure…