C k -estimates for the -equation on convex domains of finite type

For a bounded convex domain with C^∞ smooth boundary of finite type m and q=1, . . . ,n−1, we construct a -solving integral operator T*_q such that for all k ∈ ℕ and the usual C^k and -norms the operator is continuous.     

The -equation and the Hartogs phenomenon on weakly q-pseudoconcave C R manifolds

We show that the Hartogs phenomenon holds in minimal, weakly 2-pseudoconcave generic C R submanifolds of a Stein manifold with trivial normal bundle. We also prove some results concerning the local and/or global solvability of the tangential Cauchy-Riemann equations for smooth forms and currents on weakly q-pseudoconcave C R manifolds.     

Natural representations of some tilde and petersen type geometries

We determine the universal natural representations (embeddings) of certain sporadic geometries with three points per line.The final revision of this paper was done while the author held a temporary position at Michigan State University.     

Local existence theorems with estimates for\bar \partial _b on weakly pseudo-convex CR manifolds

Partially supported by NSF grants DMS 89-01455 and DMS 91-01161     

Cohomology with compact supports for cohomologically<Emphasis Type="Italic">q</Emphasis>-convex spaces

We show that if X is a complex space of dimension n which is cohomologically q-convex (resp., cohomologically q-complete), then $ H^{i}_{c} (X, \mathbb{C}) $ is a finite dimensional vector space (resp., vanishes) for $ i \leq \nu_{q}(X)-q $, where the number $ \nu_{q}(X) $ depends on the nature of singularities of X and equals n if X is smooth.     

Sur la régularitéC ∞ du\bar \partial au bord d'un domaine de ℂ n dont la forme de Levi a exactements valeurs propres strictement négatives

Sans résumé

---

     

The Poincaré-Bertrand Formula for the Bochner-Martinelli Integral

The Poincaré-Bertrand formula and the composition formula for the Bochner-Martinelli integral on piecewise smooth manifolds are obtained. As an application, the regularization problem for linear singular integral equation with Bochner-Martinelli kernel and variable coefficients is discussed.     

On the quasi-projectivity of compactifiable strongly pseudoconvex manifolds

We construct new examples of non-Kahlerian 1-convex threefolds X with exceptional set≅P₁ (resp. ≅F₂). Also the structure of Pic(X) will be studied. On the other hand, we shall investigate the quasi-projective structure of certain Kahlerian compactifiable 1-convex manifolds; particular attention will be given to 3-fold cases through concrete examples.     

An application of q-concavity to increasing sequences of Stein open sets

We prove that in a normal Stein space a relatively compact open set is a domain of holomorphy provided that it is an increasing union of Stein open subspaces. Received: 13 December 2004     

On the regularity of the leafwise Poincaré metric

We prove that for a foliation of general type on a complex projective surface the curvature of the leafwise Poincaré metric is absolutely continuous.     

Differential eigenforms

The aim of this paper is to show how differential characters of Abelian varieties (in the sense of [A. Buium, Differential characters of Abelian varieties over p-adic fields, Invent. Math. 122 (1995) 309-340]) can be used to construct differential modular forms of weight 0 and order 2 (in the sense of [A. Buium, Differential modular forms, Crelle J. 520 (2000) 95-167]) which are eigenvectors of Hecke operators. These differential modular forms will have “essentially the same” eigenvalues as certain classical complex eigenforms of weight 2 (and order 0).     

Countably determined sets and a conjecture of C.W. Henson

Partially supported by NSF grants DMS-9208071 and DMS-9100383     

An Andreotti–Vesentini separation theorem on real hypersurfaces

Using Serre duality in CR manifolds and integral operators for the solution of the tangential Cauchy–Riemann equation with compact support, we prove a separation theorem of Andreotti–Vesentini type for the -cohomology in q-concave real hypersurfaces. Received: February 17, 1999?Published online: May 10, 2001     

On the dynamics near infinity of some polynomial mappings in

We construct the Green current for a random iteration of horizontal-like mappings in . This is applied to the study of a polynomial map with the following properties: i. infinity is f-attracting; ii. f contracts the line at infinity to a point not in the indeterminacy set. We study for such mappings the escape rates near infinity, i.e. the set of possible values of the function We show in particular that the set of possible values can contain an interval. On the other hand the Green current T of f can be decomposed into pieces associated to an itinerary defined by the indeterminacy points. This allows us to prove that exists ||T||-a.e. and we give its value in terms of explicit quantities depending on f.