Prescribing the Curvature of a Riemannian Manifold

摘要: I. Gaussian Curvature Surfaces in $R^3$ Prescribing the curvature form on a surface (a) Compact surfaces (b) Noncompact II. Scalar Topological obstructions Pointwise conformal deformations and Yamabe problem $M^n$ compact noncompact scalar Cauchy-Riemann manifold III. Ricci Local solvability of Ric$(g)=R_ij$ smoothness metrics Global topological Uniqueness, nonexistence Einstein 3-manifolds Kaahler manifolds Kahler geometry Calabi's Kahler-Einstein (c) Another variational IV. Boundary Value Problems with constant mean Rellich's Some other boundary value problems Graphs prescribed Gauss The $C^2+\alpha$ estimate at Open Problems.