922 citations · 7.2k across the 348 of their papers we have counts for
6 papers · 1 filter
On exterior calculus and curvature in piecewise-flat manifolds
Jonathan R. McDonald, Warner A. Miller, Paul M. Alsing +3
Simplicial, piecewise-flat discretizations of manifolds provide a clear path towards curvature analysis on discrete geometries and for solutions of PDE's on manifolds of complex to…
Teichmüller extremal mapping and its applications to landmark matching registration
Lok Ming Lui, Ka Chun Lam, Shing-Tung Yau +1
Registration, which aims to find an optimal 1-1 correspondence between shapes, is an important process in different research areas. Conformal mappings have been widely used to obta…
Homologies of path complexes and digraphs
Alexander Grigor'yan, Yong Lin, Yuri Muranov +1
In this paper we introduce a path complex that can be regarded as a generalization of the notion of a simplicial complex. The main motivation for considering path complexes comes f…
A brief review on geometry and spectrum of graphs
Yong Lin, Shing-Tung Yau
This is a survey paper. We study the Ricci curvature and spectrum of graphs, as well as the exterior forms and deRahm cohomology on graphs.
The Geometry on Smooth Toroidal Compactifications of Siegel varieties
Shing-Tung Yau, Yi Zhang
This is a part of our joint program. The purpose of this paper is to study smooth toroidal compactifications of Siegel varieties and their applications, we also try to understand t…
Hodge Bundles on Smooth Compactifications of Siegel Varieties and Applications
Shing-Tung Yau, Yi Zhang
We study Hodge bundles on Siegel varieties and their various extensions to smooth toroidal compactifications. Precisely, we construct a canonical Hodge bundle on an arbitrary Siege…