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.

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

Domaines: Géométrie différentielle [math.DG]; Variables complexes [math.CV]; Equations aux dérivées partielles [math.AP]; Analyse fonctionnelle [math.FA]

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