S. Yau

Publications1,118
h-index102
Citations45,970
Highly Influential Citations3,643
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On The Ricci Curvature of a Compact Kahler Manifold and the Complex Monge-Ampere Equation, I*
Therefore a necessary condition for a (1,l) form ( G I a ' r r ) I,,, Rlr dz' A d? to be the Ricci form of some Kahler metric is that it must be closed and its cohomology class must represent the… Expand
On the parabolic kernel of the Schrödinger operator
Etude des equations paraboliques du type (Δ−q/x,t)−∂/∂t)u(x,t)=0 sur une variete riemannienne generale. Introduction. Estimations de gradients. Inegalites de Harnack. Majorations et minorations des… Expand
On the proof of the positive mass conjecture in general relativity
LetM be a space-time whose local mass density is non-negative everywhere. Then we prove that the total mass ofM as viewed from spatial infinity (the ADM mass) must be positive unlessM is the flat… Expand
Mirror symmetry is T duality
Abstract It is argued that every Calabi-Yau manifold X with a mirror Y admits a family of supersymmetric toroidal 3-cycles. Moreover the moduli space of such cycles together with their flat… Expand
Harmonic functions on complete riemannian manifolds
IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE
Automatic computation of surface correspondence via harmonic map is an active research field in computer vision, computer graphics and computational geometry. It may help document and understand… Expand
Calabi's conjecture and some new results in algebraic geometry.
  • S. Yau
  • Medicine, Mathematics
  • Proceedings of the National Academy of Sciences…
  • 1 May 1977
TLDR
A proof of Calabi's conjectures on the Ricci curvature of a compact Kähler manifold is announced and some new results in algebraic geometry and differential geometry are proved, including that the only Köhler structure on a complex projective space is the standard one. Expand
On the existence of hermitian‐yang‐mills connections in stable vector bundles
Differential equations on riemannian manifolds and their geometric applications
A new conformal invariant and its applications to the Willmore conjecture and the first eigenvalue of compact surfaces
Let M be a compact Riemannian manifold with a fixed conformal structure. Then we introduce the concept of conformal volume of M in the following manner. For each branched conformal immersion q9 of M… Expand
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