922 citations · 7.2k across the 348 of their papers we have counts for
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Explicit Ricci-flat metrics on a special Schoen threefold
Jixiang Fu, Jiuhe Liu, Yunyang Xiao +1
We give an explicit convergent representation of the Ricci-flat Kähler metric in a one-parameter family of classes on a fixed special Schoen threefold. The threefold resolves a shi…
Explicit Ricci-flat Metrics on Kummer K3 Surfaces
Jixiang Fu, Yunyang Xiao, Shing-Tung Yau
We give a convergent explicit representation of the Ricci-flat Kähler metrics supplied by the Calabi--Yau theorem in a one-parameter family of classes on a fixed Kummer K3 surface.…
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-…