922 citations · 7.2k across the 348 of their papers we have counts for
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Curvatures of moduli space of curves and applications
Kefeng Liu, Xiaofeng Sun, Xiaokui Yang +1
In this paper, we investigate the geometry of the moduli space of curves by using the curvature properties of direct image sheaves of vector bundles. We show that the moduli space…
Simplicial Ricci Flow: An Example of a Neck Pinch Singularity in 3D
Paul M. Alsing, Warner A. Miller, Matthew Corne +4
We examine a Type-1 neck pinch singularity in simplicial Ricci flow (SRF) for an axisymmetric piecewise flat 3-dimensional geometry with 3-sphere topology. SRF was recently introdu…
Convergence of an iterative algorithm for Teichmüller maps via generalized harmonic maps
Lui Lok Ming, Gu Xianfeng, Yau Shing-Tung
Finding surface mappings with least distortion arises from many applications in various fields. Extremal Teichmüller maps are surface mappings with least conformality distortion.…
Minimizing properties of critical points of quasi-local energy
PoNing Chen, Mu-Tao Wang, Shing-Tung Yau
In relativity, the energy of a moving particle depends on the observer, and the rest mass is the minimal energy seen among all observers. The Wang-Yau quasi-local mass for a surfac…
Simplicial Ricci Flow
Warner A. Miller, Jonathan R. McDonald, Paul M. Alsing +2
We construct a discrete form of Hamilton's Ricci flow (RF) equations for a d-dimensional piecewise flat simplicial geometry, S. These new algebraic equations are derived using the…