Smoothing q-convex functions and vanishing theorems.
Smoothing q-Convex Functions in the Singular Case.
Solution of the ?-Equation with Uniform Estimates on Strictly q-Convex Domains with Non-Smooth Boundary.
Solution of the -equation on non-smooth strictly -concave domains with Hölder estimates and the Andreotti-Vesentini separation theorem
Some applications of a new integral formula for
Let M be a smooth q-concave CR submanifold of codimension k in . We solve locally the -equation on M for (0,r)-forms, 0 ≤ r ≤ q-1 or n-k-q+1 ≤ r ≤ n-k, with sharp interior estimates in Hölder spaces. We prove the optimal regularity of the -operator on (0,q)-forms in the same spaces. We also obtain estimates at top degree. We get a jump theorem for (0,r)-forms (r ≤ q-2 or r ≥ n-k-q+1) which are CR on a smooth hypersurface of M. We prove some generalizations of the Hartogs-Bochner-Henkin extension...
Some convexity properties of morphisms of complex spaces.
Some properties of positive line bundles on 1-convex complex analytic spaces
Strongly Plurisubharmonic Exhaustion Functions on 1-Convex Spaces.
Successioni crescenti di -coppie di runge di varietà analitiche complesse
The analyticity of -concave sets of locally finite Hausdorff measure
We prove the analyticity of -concave sets of locally finite Hausdorff -measure in a -dimensional complex space. We apply it to give a removability criterion for meromorphic maps with values in -complete spaces.
The Bochner-Hartogs dichotomy for weakly 1-complete Kähler manifolds
It is proved that if is a weakly 1-complete Kähler manifold with only one end, then or there exists a proper holomorphic mapping of onto a Riemann surface.
The Bremermann-Dirichlet problem for -plurisubharmonic functions
The Hartogs-type extension theorem for meromorphic mappings into -complete complex spaces
Si dimostra un risultato di prolungamento per applicazioni meromorfe a valori in uno spazio -completo che generalizza direttamente il risultato classico di Hartogs e migliora risultati di K. Stein.
The -Cauchy problem on weakly -pseudoconvex domains in Stein manifolds
Let be a Stein manifold of complex dimension and be a relatively compact domain with smooth boundary in . Assume that is a weakly -pseudoconvex domain in . The purpose of this paper is to establish sufficient conditions for the closed range of on . Moreover, we study the -problem on . Specifically, we use the modified weight function method to study the weighted -problem with exact support in . Our method relies on the -estimates by Hörmander (1965) and by Kohn (1973).
The Levi problem for cohomology classes
In this paper we extend to complex spaces and coherent analytic sheaves some results of Andreotti and Norguet concerning the extension of cohomology classes.
The Levi Problem on Pseudoconvex Manifolds Which are not Strongly Pseudoconvex.
The -Neumann operator on Lipschitz -pseudoconvex domains
On a bounded -pseudoconvex domain in with a Lipschitz boundary, we prove that the -Neumann operator satisfies a subelliptic -estimate on and can be extended as a bounded operator from Sobolev -spaces to Sobolev -spaces.
Théorèmes de séparation et de finitude pour l’homologie et la cohomologie des espaces -convexes-concaves
Twisted sheaves on complex spaces
Über eine Vermutung von Hartshorne.