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.
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.
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.
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).
In this paper we extend to complex spaces and coherent analytic sheaves some results of Andreotti and Norguet concerning the extension of cohomology classes.
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.