Families of analytic discs in with boundaries on a prescribed submanifold
C. Denson Hill; Geraldine Taiani
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze (1978)
- Volume: 5, Issue: 2, page 327-380
- ISSN: 0391-173X
Access Full Article
topHow to cite
topHill, C. Denson, and Taiani, Geraldine. "Families of analytic discs in $\mathbf {C}^n$ with boundaries on a prescribed $CR$ submanifold." Annali della Scuola Normale Superiore di Pisa - Classe di Scienze 5.2 (1978): 327-380. <http://eudml.org/doc/83781>.
@article{Hill1978,
author = {Hill, C. Denson, Taiani, Geraldine},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
keywords = {Imbedding Analytic Discs; Implicit Function Theorem; Bishop Functional Equation; Lev Extension Phenomenon},
language = {eng},
number = {2},
pages = {327-380},
publisher = {Scuola normale superiore},
title = {Families of analytic discs in $\mathbf \{C\}^n$ with boundaries on a prescribed $CR$ submanifold},
url = {http://eudml.org/doc/83781},
volume = {5},
year = {1978},
}
TY - JOUR
AU - Hill, C. Denson
AU - Taiani, Geraldine
TI - Families of analytic discs in $\mathbf {C}^n$ with boundaries on a prescribed $CR$ submanifold
JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
PY - 1978
PB - Scuola normale superiore
VL - 5
IS - 2
SP - 327
EP - 380
LA - eng
KW - Imbedding Analytic Discs; Implicit Function Theorem; Bishop Functional Equation; Lev Extension Phenomenon
UR - http://eudml.org/doc/83781
ER -
References
top- [1] A. Andreotti - C.D. Hill - S. Łojasiewicz - B. Mackichan, Complexes of differential operators. The Mayer-Vietoris sequence, Inventiones Math., 35 (1976), pp. 43-86. Zbl0332.58016
- [2] R. Bartle, The elements of real analysis, John Wiley and Sons, New York, 1964. Zbl0116.32302MR393369
- [3] E. Bishop, Differentiable manifolds in complex Euclidean space, Duke Math. J., (1965), pp. 1-22. Zbl0154.08501MR200476
- [4] R. Courant - D. Hilbert, Methods of mathematical physics, Vol. II, Interscience Publishers, New York, 1962. Zbl0099.29504MR65391
- [5] D. Ellis - C.D. Hill - C. Seabury, The maximum modulus principle. - I: Necessary conditions, Indiana Univ. Math. J., 25 (1976), pp. 709-717. Zbl0336.32013MR590086
- [6] S.J. Greenfield, Cauchy-Riemann equations in several variables, Ann. Scuola Norm. Sup. Pisa, 22 (1968), pp. 275-314. Zbl0159.37502MR237816
- [7] C.D. Hill, A Kontinuitätssatz for ∂M and Lewy extendibility, Indiana Univ. Math. J., 22 (1972), pp. 339-347. Zbl0247.32009
- [8] C.D. Hill - B. Mackichan, Hyperf-unction cohomology classes and their boundary values, Ann. Scuola Norm. Sup. Pisa, 4 (1977), pp. 577-597. Zbl0367.46037MR467847
- [9] K. Hoffman, Banach spaces of analytic functions, Prentice-Hall, Englewood Cliffs, N. J., 1962. Zbl0117.34001MR133008
- [10] L. Hormander, An introduetion to complex analysis in several variables, Van Nostrand, Princeton, N. J., 1966. Zbl0138.06203MR203075
- [11] L.R. Hunt - R.O. Wells, Extensions of CR-functions, Amer. J. Math., 98 (1976), pp. 805-820. Zbl0334.32014MR432913
- [12] H. Lewy, On the local character of the solutions of an atypical linear differential equation in three variables and a related theorem for regular functions of two complex variables, Ann. Math., 64 (1956), pp. 514-522. Zbl0074.06204MR81952
- [13] H. Lewy, An example of a smooth linear partial differential equation without solution, Ann. Math., 66 (1957), pp. 155-158. Zbl0078.08104MR88629
- [14] H. Lewy, On hulls of holomorphy, Comm. Pure Appl. Math., 13 (1960), pp. 587-591. Zbl0113.06102MR150339
- [15] A. Nijenhuis, Strong derivatives and inverse mappings, Amer. Math. Monthly, 81 (1974), pp. 969-980. Zbl0296.58002MR360958
- [16] R. Nirenberg, On the H. Lewy extension phenomenon, Trans. Amer. Math. Soc., 168 (1972), pp. 337-356. Zbl0241.32006MR301234
- [17] M. Sato, On a generalization of the concept of functions, Proc. Japan Acad., 34 (1958), pp. 126-130 and 604-608. Zbl0080.32303MR96122
- [18] M. Sato, Theory of hyperfunctions, J. Fac. Sci., Univ. Tokyo, Sect. I, 8 (1959-60), pp. 139-193 and 387-436. Zbl0087.31402MR114124
- [19] M. Sato - T. Kawai - M. Kashiwara, Microfunctions and pseudodifferential equations, in Hyperfunctions and pseudodifferential equations, Lecture Notes in Math., 287 (1973), pp. 265-529. Zbl0277.46039MR420735
- [20] P. Schapira, Théorie des hyperfonctions, Lecture Notes in Math., 126 (1970). Zbl0192.47305MR270151
- [21] B. Weinstock, On holomorphic extension from real submanifolds of complex Euclidean space, Ph. D. Thesis, M.I.T., Cambridge, Mass., 1966.
- [22] 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. Zbl0142.33901MR197785
Citations in EuDML Documents
top- Stéphane Maingot, Sur l'extension des fonctions C R
- Eric Bedford, Stability of the polynomial hull of
- C. Denson Hill, Geraldine Taiani, Real analytic approximation of locally embeddable CR manifolds
- J.-M. Trepreau, Sur la propagation des singularités dans les variétés CR
- Eric Bedford, Levi flat hypersurfaces in with prescribed boundary : stability
- Andrea Altomani, C. Denson Hill, Mauro Nacinovich, Egmont Porten, Holomorphic extension from weakly pseudoconcave CR manifolds
- Thomas Duchamp, Edgar Lee Stout, Maximum modulus sets
- Franc Forstneric, Analytic disks with boundaries in a maximal real submanifold of
NotesEmbed ?
topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.