Families of analytic discs in 𝐂 n with boundaries on a prescribed C R 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

How to cite

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Hill, 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

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  2. [2] R. Bartle, The elements of real analysis, John Wiley and Sons, New York, 1964. Zbl0116.32302MR393369
  3. [3] E. Bishop, Differentiable manifolds in complex Euclidean space, Duke Math. J., (1965), pp. 1-22. Zbl0154.08501MR200476
  4. [4] R. Courant - D. Hilbert, Methods of mathematical physics, Vol. II, Interscience Publishers, New York, 1962. Zbl0099.29504MR65391
  5. [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. [6] S.J. Greenfield, Cauchy-Riemann equations in several variables, Ann. Scuola Norm. Sup. Pisa, 22 (1968), pp. 275-314. Zbl0159.37502MR237816
  7. [7] C.D. Hill, A Kontinuitätssatz for ∂M and Lewy extendibility, Indiana Univ. Math. J., 22 (1972), pp. 339-347. Zbl0247.32009
  8. [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. [9] K. Hoffman, Banach spaces of analytic functions, Prentice-Hall, Englewood Cliffs, N. J., 1962. Zbl0117.34001MR133008
  10. [10] L. Hormander, An introduetion to complex analysis in several variables, Van Nostrand, Princeton, N. J., 1966. Zbl0138.06203MR203075
  11. [11] L.R. Hunt - R.O. Wells, Extensions of CR-functions, Amer. J. Math., 98 (1976), pp. 805-820. Zbl0334.32014MR432913
  12. [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. [13] H. Lewy, An example of a smooth linear partial differential equation without solution, Ann. Math., 66 (1957), pp. 155-158. Zbl0078.08104MR88629
  14. [14] H. Lewy, On hulls of holomorphy, Comm. Pure Appl. Math., 13 (1960), pp. 587-591. Zbl0113.06102MR150339
  15. [15] A. Nijenhuis, Strong derivatives and inverse mappings, Amer. Math. Monthly, 81 (1974), pp. 969-980. Zbl0296.58002MR360958
  16. [16] R. Nirenberg, On the H. Lewy extension phenomenon, Trans. Amer. Math. Soc., 168 (1972), pp. 337-356. Zbl0241.32006MR301234
  17. [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. [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. [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. [20] P. Schapira, Théorie des hyperfonctions, Lecture Notes in Math., 126 (1970). Zbl0192.47305MR270151
  21. [21] B. Weinstock, On holomorphic extension from real submanifolds of complex Euclidean space, Ph. D. Thesis, M.I.T., Cambridge, Mass., 1966. 
  22. [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

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  1. Stéphane Maingot, Sur l'extension des fonctions C R
  2. Eric Bedford, Stability of the polynomial hull of T 2
  3. C. Denson Hill, Geraldine Taiani, Real analytic approximation of locally embeddable CR manifolds
  4. J.-M. Trepreau, Sur la propagation des singularités dans les variétés CR
  5. Eric Bedford, Levi flat hypersurfaces in C 2 with prescribed boundary : stability
  6. Andrea Altomani, C. Denson Hill, Mauro Nacinovich, Egmont Porten, Holomorphic extension from weakly pseudoconcave CR manifolds
  7. Thomas Duchamp, Edgar Lee Stout, Maximum modulus sets
  8. Franc Forstneric, Analytic disks with boundaries in a maximal real submanifold of 𝐂 2

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