Courants de type Liouville pour les applications holomorphes

Abstract

We show that every regularized positif closed current T with slow growth on a Kähler manifold M is a Liouville current with respect to the class of holomorphic maps bounded on the support of T with values on a Kähler manifold N whose Kähler form is exact. We establish a Casorati–Weierstrass type theorem for the current T. Also we show that if ( M, ω) is a complete Kähler manifold with nonnegative Ricci curvature at infinity, i.e., Ric ω ( x)⩾− α( r( x)) where α( t) is nonnegative and decreass to 0 at infinity, then M is a Liouville manifold provided that λ 1( M)⩾ pα(0) and the function max( α( r), r −2) is p-summable at infinity for some p>1. To cite this article: S. Asserda, M. Kassi, C. R. Acad. Sci. Paris, Ser. I 335 (2002) 751–756.