We generalize classical results for plurisubharmonic functions and hyperconvex domain to q-plurisubharmonic functions and q-hyperconvex domains. We show, among other things, that Bq-regular domains are q-hyperconvex. Moreover, some smoothing results for q-plurisubharmonic functions are also given.
Let be a bounded pseudoconvex domain that admits a Hölder continuous plurisubharmonic exhaustion function. Let its pluricomplex Green function be denoted by . In this article we give for a compact subset a quantitative upper bound for the supremum in terms of the boundary distance of and . This enables us to prove that, on a smooth bounded regular domain (in the sense of Diederich-Fornaess), the Bergman differential metric tends to infinity, for , when tends to a boundary point....
We prove the invariance of hyperbolic imbeddability under holomorphic fiber bundles with compact hyperbolic fibers. Moreover, we show an example concerning the relation between the Kobayashi relative intrinsic pseudo-distance of a holomorphic fiber bundle and the one in its base.
On résout le pour les formes admettant une valeur au bord au sens des courants sur un domaine strictement pseudoconvexe de .
The definition of the Kobayashi-Royden pseudo-metric for almost complex manifolds is similar to its definition for complex manifolds. We study the question of completeness of some domains for this metric. In particular, we study the completeness of the complement of submanifolds of co-dimension 1 or 2. The paper includes a discussion, with proofs, of basic facts in the theory of pseudo-holomorphic discs.
is compact and convex it is known for a long time that the nonzero constant coefficients linear partial differential operators (of finite or infinite order) are surjective on the space of all analytic functions on G. We consider the question whether solutions of the inhomogeneous equation can be given in terms of a continuous linear operator. For instance we characterize those sets G for which this is always the case.