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On The Ricci Curvature of a Compact Kahler Manifold and the Complex Monge-Ampere Equation, I*
- S. Yau
- 1 May 1978
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…
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…
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…
Mirror symmetry is T duality
IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE
This work conquers the constrained surface registration problem by changing the Riemannian metric on the target surface to a hyperbolic metric so that the harmonic mapping is guaranteed to be a diffeomorphism under landmark constraints.
Harmonic functions on complete riemannian manifolds
- S. Yau
- 1 March 1975
Calabi's conjecture and some new results in algebraic geometry.
- S. Yau
- MathematicsProceedings 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.
On the existence of hermitian‐yang‐mills connections in stable vector bundles
Differential equations on riemannian manifolds and their geometric applications