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Recent Development on the Geometry of the Teichmuller and Moduli Spaces of Riemann Surfaces and Polarized Calabi-Yau Manifolds
Kefeng Liu, Xiaofeng Sun, Shing-Tung Yau
We survey our recent new results on the geometry of Teichmuller and moduli spaces of Riemann surfaces and Calabi-Yau manifolds.
Limit of quasilocal mass at spatial infinity
Mu-Tao Wang, Shing-Tung Yau
We study the limit of quasilocal mass defined in [4] and [5] for a family of spacelike 2-surfaces in spacetime. In particular, we show the limit coincides with the ADM mass at spat…
Gap of the First Two Eigenvalues of the Schrödinger Operator with Nonconvex Potential
Shing-Tung Yau
We give a lower estimate of the gap of the first two eigenvalues of the Schrodinger operator with a nonconvex potential in terms of a distance associated with the potential. The re…
An Estimate of the Gap of the First Two Eigenvalues in the Schrödinger Operator
Shing-Tung Yau
We give a lower estimate of the gap of the first two eigenvalues of the Schrodinger operator in the case when the potential is strongly convex. In particular, if the Hessian of the…