922 citations · 7.2k across the 348 of their papers we have counts for
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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.…
Counting higher-rank sheaves on toric threefolds
Nicolo Piazzalunga, Artan Sheshmani, Shing-Tung Yau
We develop an equivariant K-theoretic vertex formalism for a colored, abelianized higher-rank sector on smooth projective toric threefolds . Nonzero first Chern classes are enco…
Stability of the Cotangent Bundle on Surfaces with Ample Canonical Class
Tristan C. Collins, Jason Lo, Yun Shi +1
In this article, we study the Bridgeland stability of the cotangent bundle on K3 surfaces and surfaces with ample canonical class. On a surface with ample canonical class ,…
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…