No abstract

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 {fm} m≥1 be a sequence of holomorphic functions defined on a bounded domain D ⊂ C n or a sequence of rational functions (1 ≤ deg rm ≤ m) defined on C n . We are interested in finding sufficient conditions to ensure the convergence of {fm} m≥1 on a large set provided the convergence holds pointwise on a not too small set. This type of result is inspired from a theorem of Vitali which gives a positive answer for uniformly bounded sequence.

No abstract

In this note by using techniques similar to that of [2] and [3], we study the local polynomial convexity of perturbation of union of two totally real planes meeting along a real line.