922 citations · 7.2k across the 348 of their papers we have counts for
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Null Asymptotics of Solutions of the Einstein-Maxwell Equations in General Relativity and Gravitational Radiation
Lydia Bieri, PoNing Chen, Shing-Tung Yau
We prove that for spacetimes solving the Einstein-Maxwell (EM) equations, the electromagnetic field contributes at highest order to the nonlinear memory effect of gravitational wav…
D-branes of A-type, their deformations, and Morse cobordism of A-branes on Calabi-Yau 3-folds under a split attractor flow: Donaldson/Alexander-Hilden-Lozano-Montesinos-Thurston/Hurwitz/Denef-Joyce meeting Polchinski-Grothendieck
Chien-Hao Liu, Shing-Tung Yau
In [L-Y5] (D(6): arXiv:1003.1178 [math.SG]) we introduced the notion of Azumaya -manifolds with a fundamental module and morphisms therefrom to a complex manifold. In t…
Cohomology and Hodge Theory on Symplectic Manifolds: II
Li-Sheng Tseng, Shing-Tung Yau
We show that the exterior derivative operator on a symplectic manifold has a natural decomposition into two linear differential operators, analogous to the Dolbeault operators in c…
Finiteness of Subfamilies of Calabi-Yau n-Folds over Curves with Maximal Length of Yukawa-Coupling
Kefeng Liu, Andrey Todorov, Shing-Tung Yau +1
We give a simplified and more algebraic proof of the finiteness of the families of Calabi-Yau n-folds with non-vanishing of Yukawa-coupling over a fixed base curve and with fixed d…
Optimization of Surface Registrations using Beltrami Holomorphic Flow
L. M. Lui, T. W. Wong, W. Zeng +4
In shape analysis, finding an optimal 1-1 correspondence between surfaces within a large class of admissible bijective mappings is of great importance. Such process is called surfa…
D-branes and Azumaya noncommutative geometry: From Polchinski to Grothendieck
Chien-Hao Liu, Shing-Tung Yau
We review first Azumaya geometry and D-branes in the realm of algebraic geometry along the line of Polchinski-Grothendieck Ansatz from our earlier work and then use it as backgroun…