273 citations · 1.6k across the 172 of their papers we have counts for
267 papers
Positive Sectional Curvature on All Smooth 7-spheres
Yang-Hui He, Ziran Liu, Shing-Tung Yau
We construct a smooth Riemannian metric with strictly positive sectional curvature on every smooth homotopy seven-sphere. For each smooth structure, we construct positively curved…
Divisorial Rigidity and Regularity of Boundary Cases for the Supercritical LYZ Equation
Jixiang Fu, Shing-Tung Yau, Dekai Zhang +1
We study the supercritical LYZ equation on compact Kähler manifolds at the boundary of stability. Under numerical semistability, we prove a quantitative positivity estimate on the…
Compact Proof of the Positivity of Quasi-Local Masses for a class of Initial Data
Puskar Mondal, Shing-Tung Yau
We prove a purely quasi-local positivity theorem for the Wang--Yau mass for a class of initial data whose Jang deformation, after a boundary-preserving conformal reduction to zero…
On Compact Hermitian Surfaces With Positive Strominger-Bismut Sectional Curvature
Qingsong Wang, Shing-Tung Yau, Fangyang Zheng
In an earlier work, Yau and Zheng proposed a Hermitian analogue of a weak form of the Frankel conjecture, which states that any compact Hermitian manifold with positive Strominger-…
Orthogonal complex structures on flat tori
Qingsong Wang, Shing-Tung Yau, Fangyang Zheng
We classify compact Hermitian manifolds with flat Levi-Civita connection. This is equivalent to the classification of all orthogonal complex structures on flat tori. It generalized…
Boundary-Geometry-Driven Black Hole Formation in Vacuum
Dipanjan Dey, Puskar Mondal, Shing-Tung Yau
We identify a boundary-geometry-driven mechanism for the dynamical formation of marginally outer trapped surfaces (MOTSs) in vacuum general relativity. Mild three-dimensional aniso…