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-…
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…
Volume Stability for Hyperbolic Manifolds and Applications to General Relativity
Puskar Mondal, Shing-Tung Yau
We prove a sharp volume-stability theorem for closed hyperbolic three-manifolds. Let \((M,h)\) be closed hyperbolic with \(\operatorname{Ric}_h=-2h\), and let \(g_i\) be smooth met…