Summary
In this work the authors prove that all sufficiently small analytic discs in the tangent space of a non generic embedded CR manifold M′⊂CN (M′ at least of class C4) can be lifted uniquely to analytic discs in CN with boundaries on M′ Moreover if M′ is real analytic or C∞ then real analytic or C∞ discs lift without loss of derivatives. If M′ is of class CK then there is a 1+ε loss of derivatives in the lifting. A stability result is also proven.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
Bibliografia
A. Andreotti -C. D. Hill,Complex characteristic coordinates and tangential Cauchy-Riemann equations, Ann. Scuola Norm. Sup. Pisa,26 (1972), pp. 299–324.
E. Bishop,Differential manifolds in complex Euclidean space, Duke Math. J.,32 (1965), pp. 1–22.
R. Courant -D. Hilbert,Methods of mathematical physics, vol. II, Interscience Publishers, New York, 1962.
J. Dieudonné,Éléments d'analyse, vol. I, Cahiers scientifiques, Gauthier-Villars, Paris, 1969.
S. J. Greenfield,Cauchy-Riemann equations in several variables, Ann. Scuola Norm. Sup. Pisa,22 (1968), pp. 275–314.
C. D. Hill -G. Taiani,Families of analytic discs in C n with boundaries on a prescribed CR submanifold, Ann. Scuola Norm. Sup. Pisa,2 (1978), pp. 327–380.
C. D.Hill - G.Taiani,The local family of analytic discs attached to a CR submanifold, Proceeding of International Conferences, Cortona, Italy 1976–77, pp. 166–179.
C. D.Hill - G.Taiani,On the H. Lewy extension phenomenon in higher codimension, in pubblicazioue.
C. D.Hill - G.Taiani,Real analytic approximation of embeddable CR manifolds, in pubblicazione.
H. R. Hunt -R. O. Wells,Extensions of CR-functions, Amer. Math. J.,98 (1976), pp. 805–820.
H. R. Hunt -R. O. Wells,Holomorphic extension for non-generic CR-submanifolds, Proc. Symp. Pure Math.,27 (1975), pp. 81–88.
G. Tomassini,Tracce delle funzioni olomorfe sulle sottovarietà analitiche reali d'una varietà complessa, Ann. Scuola Norm. Sup. Pisa,20 (1966), pp. 31–43.
B. Weinstock,On holomorphic extension from real submanifolds of complex Euclidean space, Ph. D. Thesis, M.I.T., Cambridge, Mass., 1966.
R. O. Wells,On the local holomorphic hull of a real submanifold in several complex variables, Comm. Pure Appl. Math.,19 (1966), pp. 145–165.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Primicerio, A.S., Taiani, G. Famiglie di dischi analitici con bordo su sottovarietàCR non generiche. Annali di Matematica pura ed applicata 126, 233–251 (1980). https://doi.org/10.1007/BF01762509
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01762509