Annali di Matematica Pura ed Applicata

, Volume 171, Issue 1, pp 159–179 | Cite as

On the Cauchy problem in complex analysis

  • C. Denson Hill
  • Mauro Nacinovich


Cauchy Problem Complex Analysis 
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  1. [AjHe]
    R. A. Ajrapetyan -G. M. Henkin,Integral representations of differential forms on Cauchy-Riemann manifolds and the theory of CR functions I, II, Usp. Mat. Nauk,39, n. 3 (1984), pp. 39–106; English transl.: Russ. Math. Surv.,39, n. 3 (1984), pp. 41–118; Mat. Sb. Nov. Ser.,127, n. 1 (1985), pp. 92–112; English transl.: Math. USSR, Sb.,55, n. 1 (1986), pp. 91–111.Google Scholar
  2. [AFN]
    A. Andreotti -G. A. Fredricks -M. Nacinovich,On the absence of Poincaré lemma in tangential Cauchy-Riemann complexes, Ann. Scuola Norm. Sup. Pisa,8 (1981), pp. 365–404.Google Scholar
  3. [AG]
    A. Andreotti -H. Grauert,Théorèmes des finitude pour la cohomologie des espaces complexes, Bull. Soc. Math. France,90 (1962), pp. 193–259.Google Scholar
  4. [AH]
    A. Andreotti -C. D. Hill,E. E. Levi convexity and the Hans Lewy problem I, II, Ann. Scuola Norm. Sup. Pisa,26 (1972), pp. 325–363, 747–806.Google Scholar
  5. [AHLM]
    A. Andreotti -C. D. Hill -S. Lojasiewicz -B. MacKichan,Complexes of partial differential operators: The Mayer-Vietoris sequence, Invent. Math.,26 (1976), pp. 43–86.Google Scholar
  6. [BP]
    A. Boggess -J. Polking,Holomorphic extension of CR functions, Duke Math. J.,49 (1982), pp. 757–784.Google Scholar
  7. [BT]
    M. S. Baouendi -F. Treves,A property of the functions and distributions annihilated by a locally integrable system of complex vector fields, Ann. Math.,113 (1981), pp. 387–421.Google Scholar
  8. [G]
    R. Godement,Topologie algébrique et théorie des faisceaux, Hermann, Paris (1958).Google Scholar
  9. [HN1]
    C. D. Hill -M. Nacinovich,Pseudoconcave CR manifolds, Dipartimento di Matematica, Pisa (Feb. 1993), pp. 1–36;Complex Analysis and Geometry, Lecture Notes in Pure and Appl. Math., v.173, pp. 275–297, Marcel Dekker, New York (1996).Google Scholar
  10. [HN2]
    C. D. Hill -M. Nacinovich,Aneurysms of pseudoconcave CR manifolds, Dipartimento di Matematica, Pisa, 1.83 (745) (Jun. 1993), pp. 1–22;Math. Z.,220 (1995), pp. 347–367.Google Scholar
  11. [HN3]
    C. D. Hill -M. Nacinovich,Duality and distribution cohomology of CR manifolds, Dipartimento di Matematica, Pisa (Feb. 1994), pp. 1–26; Ann. Scuola Norm. Sup. Pisa,22 (1995), pp. 315–339.Google Scholar
  12. [HN4]
    C. D. Hill -M. Nacinovich,The topology of Stein CR manifolds and the Lefschetz theorem, Ann. Inst. Fourier Grenoble,43, 2 (1993), pp. 459–468.Google Scholar
  13. [L]
    H. Laufer,On the infinite dimensionality of the Dolbeauit cohomology groups, Proc. AMS,52 (1975), pp. 293–296.Google Scholar
  14. [L-TL1]
    C. Laurent-Thiébaut -J. Leiterer,Théorie d'Andreotti-Grauert pour les hypersurfaces réelies d'une variété analytique complexe, C. R. Acad. Sci. Paris, série I,316 (1993), pp. 891–894.Google Scholar
  15. [L-TL2]
    C. Laurent-Thiébaut -J. Leiterer,Uniform estimates for the Cauchy-Riemann equations on q-pseudoconvex wedges, Ann. Inst. Frourier Grenoble,43 (1993), pp. 383–436.Google Scholar
  16. [L-TL3]
    C.Laurent-Thiébaut - J.Leiterer,Andreotti-Grauert theory on real hypersurfaces, I. The q-convex case, Prép. Inst. Fourier Grenoble,253 (1993).Google Scholar
  17. [L-TL4]
    C.Laurent-Thiébaut - J.Leiterer,On the Cauchy-Riemann equations in q-concave wedges, Prép. Inst. Fourier Grenoble,289 (1994).Google Scholar
  18. [L-TL5]
    C.Laurent-Thiébaut - J.Leiterer,Andreotti-Grauert theory on real hypersurfaces, II. The q-concave case, Prép. Inst. Fourier Grenoble,280 (1994).Google Scholar
  19. [MN]
    C. Medori -M. Nacinovich,Pluriharmonic functions on abstract CR manifolds, Dipartimento di Matematica, Pisa, 1.78 (727) (Mar. 1993), pp. 1–16.Google Scholar
  20. [N1]
    M. Nacinovich,Poincaré lemma for tangential Cauchy-Riemann complexes, Math. Ann.,268 (1984), pp. 449–471.Google Scholar
  21. [N2]
    M. Nacinovich,On strict Levi q-convexity and q-concavity of domains with piecewise smooth boundaries, Math. Ann.,281 (1988), pp. 459–482.Google Scholar
  22. [N3]
    M.Nacinovich,On a theorem of Ajrapetyan and Henkin, Seminari di Geometria 1988–1991, Univ. Bologna, pp. 99–135.Google Scholar
  23. [N4]
    M. Nacinovich,Cauchy problem for overdetermined systems, Ann. Mat. Pura Appl.,156 (1990), pp. 265–321.Google Scholar
  24. [N5]
    M. Nacinovich,Overdetermined hyperbolic systems on l.e. convex sets, Rend. Sem. Mat. Univ. Padova,83 (1990), pp. 107–132.Google Scholar
  25. [NV]
    M. Nacinovich -G. Valli,Tangential Cauchy-Riemann complexes on distributions, Ann. Mat. Pura Appl.,146 (1987), pp. 123–160.Google Scholar
  26. [T]
    J. C. Tougeron,Ideaux de fonctions differentiables, Springer, Berlin, Heidelberg, New York (1972).Google Scholar

Copyright information

© Fondazione Annali di Matematica Pura ed Applicata 1996

Authors and Affiliations

  • C. Denson Hill
    • 2
  • Mauro Nacinovich
    • 1
  1. 1.Dipartimento di MatematicaPisa
  2. 2.Department of MathematicsSUNY at Stone BrookStone BrookUSA

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