Gigante, Tomassini: Foliations with complex leaves

Gigante, Giuliana and Tomassini, Giuseppe:
Foliations with complex leaves (Foliazioni con foglie complesse)
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni Serie 9 4 (1993), fasc. n.2, p. 115-120, (English)
pdf (692 Kb), djvu (137 Kb). | MR1233399 | Zbl 0784.32027

Sunto

Sia \( X \) una varietà differenziabile fogliata con foglie complesse e sia \( \mathcal{D} \) il fascio dei germi delle funzioni differenziabili su \( X \), olomorfe lungo le foglie. Si studia lo spazio anellato \( (X, \mathcal{D}) \); in particolare la teoria delle funzioni per l'algebra \( \mathcal{D}(X) \) e la coomologia a valori in \( \mathcal{D} \).

Referenze Bibliografiche

[1] A. ANDREOTTI - H. GRAUERT, Théorèmes de finitude pour la cohomologie des espaces complexes. Bull. Soc. Math. France, 90, 1962, 193-259. | fulltext EuDML | fulltext mini-dml | MR 150342 | Zbl 0106.05501

[2] A. ANDREOTTI - M. NACINOVICH, Analytic Convexity. Ann. Scuola Norm. Sup. Pisa, 7, 1980, 287-372. | fulltext EuDML | fulltext mini-dml | MR 581145 | Zbl 0435.35039

[3] J. CHAUMAT - A. M. CHOLLET, Noyaux pour résoudre l'équation \( \bar{\partial} \) dans des classes ultradifférentiables sur des compacts irréguliers de \( \mathbb{C}^{n} \). Preprint.

[4] M. FREEMAN, Local complex foliations of real submanifolds. Math. Ann., 209, 1970, 1-30. | fulltext EuDML | MR 346185 | Zbl 0267.32006

[5] M. FREEMAN, Tangential Cauchy-Riemann equations and uniform approximation. Pacific J. Math., 33, N. 1, 1970, 101-108. | fulltext mini-dml | MR 264117 | Zbl 0184.31103

[6] R. GAY - A. SEBBAR, Division et extension dans l'algèbre \( A^{\infty}(\Omega) \) d'un ouvert pseudo-convex à bord lisse de \( \mathbb{C}^{n} \). Math. Z., 189, 1985, 421-447. | fulltext EuDML | fulltext (doi) | MR 783566 | Zbl 0547.32009

[7] L. HÖRMANDER, An Introduction to Complex Analysis in Several Variables. North-Holland 1973. | MR 1045639 | Zbl 0271.32001

[8] S. KOBAYASHI, Intrinsic distances, measures and geometric function theory. Bull. Am. Math. Soc., 82, 1976, 357-416. | fulltext mini-dml | MR 414940 | Zbl 0346.32031

[9] J. J. KOHN, Global regularity for \( \bar{\partial} \) on weakly pseudoconvex manifolds. Trans. Amer. Math. Soc., 181, 1973, 273-292. | MR 344703 | Zbl 0276.35071

[10] L. NIRENBERG, A Proof of the Malgrange Preparation Theorem. Proceedings of Liverpool Singularities, I. Lecture notes in mathematics, 192, Springer-Verlag, New York 1971, 97-105. | MR 412460 | Zbl 0212.10702

[11] C. REA, Levi flat submanifolds and biholomorphic extension of foliations. Ann. Scuola Norm. Sup. Pisa, 26, 1972, 664-681. | fulltext EuDML | fulltext mini-dml | MR 425158 | Zbl 0272.57013

[12] N. SIBONY, A class of hyperbolic manifolds. Recent developments in several complex variables. Ann. of Math. Stud., Princeton Univ. Press, N. 100, 1981. | MR 627768 | Zbl 0476.32033

[13] F. SOMMER, Komplexe analytische Blätterung reeler Mannigfaltigkeiten in \( \mathbb{C}^{n} \). Math. Ann., 136, 1958, 111-133. | fulltext EuDML | MR 101924 | Zbl 0092.29902

[14] G. TOMASSINI, Extension d'objects CR. Math. Z., 194, 1987, 471-486. | fulltext EuDML | fulltext (doi) | MR 881705 | Zbl 0629.32015

bdim: Biblioteca Digitale Italiana di Matematica

Un progetto SIMAI e UMI

Referenza completa

Sunto

Referenze Bibliografiche