35 citations · 116 across the 20 of their papers we have counts for
20 papers
Strengthened Euler's Inequality in Spherical and Hyperbolic Geometries
Ren Guo, Estonia Black, Caleb Smith
Euler's inequality is a well known inequality relating the inradius and circumradius of a triangle. In Euclidean geometry, this inequality takes the form where is t…
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…
The Unified Surface Ricci Flow
Min Zhang, Ren Guo, Wei Zeng +3
Ricci flow deforms the Riemannian metric proportionally to the curvature, such that the curvature evolves according to a heat diffusion process and eventually becomes constant ever…
A survey of quantum Teichmüller space and Kashaev algebra
Ren Guo
In this chapter, we survey the algebraic aspects of quantum Teichmüller space, generalized Kashaev algebra and a natural relationship between the two algebras.
Extremum problems for eigenvalues of discrete Laplace operators
Ren Guo
The discrete Laplace operator on a triangulated polyhedral surface is related to geometric properties of the surface. This paper studies extremum problems for eigenvalues of the di…
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…