1 citations · 1 across the 4 of their papers we have counts for
4 papers
Hodge rigidity of Chern classes
Yuxiang Liu, Artan Sheshmani, Shing-Tung Yau
In this paper, we study the homogeneous components of the Chern--Schwartz--MacPherson (CSM) classes of Schubert cells. We prove that, under suitable conditions, each such component…
A Proof of the Eigenvalue Ratio Bound for Embedded Surfaces
Ricardo Gloria-Picazzo, Yingying Wu, Shing-Tung Yau
We explain how the spectrum of a closed embedded surface relates to the Dirichlet spectrum of the bounded domain with $\partial Ω= Σ…
Microlocal index theorems and analytic torsion invariants in the geometric theory of partial differential equations
Jacob Kryczka, Vladimir Rubtsov, Artan Sheshmani +1
We develop a microlocal and derived-geometric framework for index theory and analytic torsion of nonlinear PDEs. By integrating Spencer hypercohomology, microlocal sheaf theory, an…
Harnack inequalities for graphs with non-negative Ricci curvature
Fan Chung, Yong Lin, Shing-Tung Yau
We establish a Harnack inequality for finite connected graphs with non-negative Ricci curvature. As a consequence, we derive an eigenvalue lower bound, extending previous results f…