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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 theExpand
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 desExpand
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 flatExpand
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 flatExpand
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 understandExpand
Calabi's conjecture and some new results in algebraic geometry.
  • S. Yau
  • Medicine, Mathematics
  • Proceedings of the National Academy of Sciences…
  • 1 May 1977
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
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 MExpand