34 citations · 226 across the 51 of their papers we have counts for
7 papers · 1 filter
Discrete Laplace-Beltrami Operator Determines Discrete Riemannian Metric
Xianfeng David Gu, Ren Guo, Feng Luo +1
The Laplace-Beltrami operator of a smooth Riemannian manifold is determined by the Riemannian metric. Conversely, the heat kernel constructed from its eigenvalues and eigenfunction…
A note on complete hyperbolic structures on ideal triangulated 3-manifolds
Feng Luo
It is a theorem of Casson and Rivin that the complete hyperbolic metric on a cusp end ideal triangulated 3-manifold maximizes volume in the space of all positive angle structures.…
Rigidity of Polyhedral Surfaces, III
Feng Luo
This paper investigates several global rigidity issues for polyhedral surfaces including inversive distance circle packings. Inversive distance circle packings are polyhedral surfa…
Cell decompositions of Teichmüller spaces of surfaces with boundary
Ren Guo, Feng Luo
A family of coordinates for the Teichmüller space of a compact surface with boundary was introduced in \cite{l2}. In the work \cite{m1}, Mondello showed that the coordinate $…
Computing Quasiconformal Maps on Riemann surfaces using Discrete Curvature Flow
W. Zeng, L. M. Lui, F. Luo +4
Surface mapping plays an important role in geometric processing. They induce both area and angular distortions. If the angular distortion is bounded, the mapping is called a {\it q…
Thurston's Spinning Construction and Solutions to the Hyperbolic Gluing Equations for Closed Hyperbolic 3-Manifolds
Feng Luo, Stephan Tillmann, Tian Yang
We show that the hyperbolic structure on a closed, orientable, hyperbolic 3-manifold can be constructed from a solution to the hyperbolic gluing equations using any triangulation w…
Triangulated 3-Manifolds: from Haken's normal surfaces to Thurston's algebraic equation
Feng Luo
We give a brief summary of some of our work and our joint work with Stephan Tillmann on solving Thurston's equation and Haken equation on triangulated 3-manifolds in this paper. Se…