922 citations · 7.2k across the 348 of their papers we have counts for
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A special Lagrangian type equation for holomorphic line bundles
Adam Jacob, Shing-Tung Yau
Let be a holomorphic line bundle over a compact Kähler manifold . Motivated by mirror symmetry, we study the deformed Hermitian-Yang-Mills equation on , which is the line…
Volume doubling, Poincaré inequality and Guassian heat kernel estimate for nonnegative curvature graphs
Paul Horn, Yong Lin, Shuang Liu +1
By studying the heat semigroup, we prove Li-Yau type estimates for bounded and positive solutions of the heat equation on graphs, under the assumption of the curvature-dimension in…
Conserved quantities on asymptotically hyperbolic initial data sets
Po-Ning Chen, Mu-Tao Wang, Shing-Tung Yau
In this article, we consider the limit of quasi-local conserved quantities [31,9] at the infinity of an asymptotically hyperbolic initial data set in general relativity. These give…
Non-Kaehler SYZ mirror symmetry
Siu-Cheong Lau, Li-Sheng Tseng, Shing-Tung Yau
We study SYZ mirror symmetry in the context of non-Kaehler Calabi-Yau manifolds. In particular, we study the six-dimensional Type II supersymmetric systems with Ramond-Ramo…
D-branes and Azumaya/matrix noncommutative differential geometry, I: D-branes as fundamental objects in string theory and differentiable maps from Azumaya/matrix manifolds with a fundamental module to real manifolds
Chien-Hao Liu, Shing-Tung Yau
We consider D-branes in string theory and address the issue of how to describe them mathematically as a fundamental object (as opposed to a solitonic object) of string theory in th…
Poisson metrics on flat vector bundles over non-compact curves
Tristan C. Collins, Adam Jacob, Shing-Tung Yau
Let (E,D,P) be a flat vector bundle with a parabolic structure over a punctured Riemann surface, (M,g). We consider a deformation of the harmonic metric equation which we call the…