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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
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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
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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
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On the Schrödinger equation and the eigenvalue problem
AbstractIf λk is thekth eigenvalue for the Dirichlet boundary problem on a bounded domain in ℝn, H. Weyl's asymptotic formula asserts that $$\lambda _k \sim C_n \left( {\frac{k}{{V(D)}}}Expand
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Hypersurfaces with constant scalar curvature
Let M be a complete two-dimensional surface immersed into the three-dimensional Euclidean space. Then a classical theorem of Hilbert says that when the curvature of M is a non-zero constant, M mustExpand
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