Convexity of the Set of k-Admissible Functions on a Compact Kähler Manifold.

Asma Jbilou (1)

1 JAD - Laboratoire Jean Alexandre Dieudonné

We prove in this article using some convex analysis results of A. S. Lewis the log-concavity of spectral elementary symmetric functions on the space of Hermitian matrices, and the convexity of the set of k-admissible functions on compact Kähler manifolds.

Keywords: Spectral Functions; Log-concavity; Convexity; Admissible Functions; Hessian Equations; Kähler Manifolds.; Kähler Manifolds

Domains: Differential Geometry [math.DG]; Complex Variables [math.CV]; Analysis of PDEs [math.AP]; Functional Analysis [math.FA]

Asma Jbilou. Convexity of the Set of k-Admissible Functions on a Compact Kähler Manifold.. 2012. ⟨hal-00694502⟩