Complex Hessian Equations on Some Compact Kähler Manifolds

Abstract EN

On a compact connected 2m-dimensional Kähler manifold with Kähler form ω, given a smooth function f:M→ℝ and an integer 1

We solve by the continuity method the corresponding complex elliptic kth Hessian equation, more difficult to solve than the Calabi-Yau equation (k=m), under the assumption that the holomorphic bisectional curvature of the manifold is nonnegative, required here only to derive an a priori eigenvalues pinching.