922 citations · 7.2k across the 348 of their papers we have counts for
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The deformed Hermitian-Yang-Mills equation in geometry and physics
Tristan C. Collins, Dan Xie, Shing-Tung Yau
We provide an introduction to the mathematics and physics of the deformed Hermitian-Yang-Mills equation, a fully nonlinear geometric PDE on Kahler manifolds which plays an importan…
Invariant metrics on negatively pinched complete Kähler manifolds
Damin Wu, Shing-Tung Yau
We prove that a complete Kähler manifold with holomorphic curvature bounded between two negative constants admits a unique complete Kähler-Einstein metric. We also show this metric…
Further studies of the notion of differentiable maps from Azumaya/matrix supermanifolds I. The smooth case: Ramond-Neveu-Schwarz and Green-Schwarz meeting Grothendieck
Chien-Hao Liu, Shing-Tung Yau
In this sequel to works D(11.1) (arXiv:1406.0929 [math.DG]), D(11.2) (arXiv:1412.0771 [hep-th]), and D(11.3.1) (arXiv:1508.02347 [math.DG]), we re-examine --- and reformulate when…
A Realization of Thurstons Geometrization: Discrete Ricci Flow with Surgery
Paul M. Alsing, Warner A. Miller, Shing-Tung Yau
Hamilton's Ricci flow (RF) equations were recently expressed in terms of a sparsely-coupled system of autonomous first-order nonlinear differential equations for the edge lengths o…
Positive Scalar Curvature and Minimal Hypersurface Singularities
Richard Schoen, Shing-Tung Yau
In this paper we develop methods to extend the minimal hypersurface approach to positive scalar curvature problems to all dimensions. This includes a proof of the positive mass the…