Levi flat hypersurfaces in C 2 with prescribed boundary : stability

Eric Bedford

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze (1982)

  • Volume: 9, Issue: 4, page 529-570
  • ISSN: 0391-173X

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Bedford, Eric. "Levi flat hypersurfaces in $C^2$ with prescribed boundary : stability." Annali della Scuola Normale Superiore di Pisa - Classe di Scienze 9.4 (1982): 529-570. <http://eudml.org/doc/83891>.

@article{Bedford1982,
author = {Bedford, Eric},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
keywords = {strictly pseudoconvex domain; Levi-flat hypersurface; stability theorem; polynomial hull},
language = {eng},
number = {4},
pages = {529-570},
publisher = {Scuola normale superiore},
title = {Levi flat hypersurfaces in $C^2$ with prescribed boundary : stability},
url = {http://eudml.org/doc/83891},
volume = {9},
year = {1982},
}

TY - JOUR
AU - Bedford, Eric
TI - Levi flat hypersurfaces in $C^2$ with prescribed boundary : stability
JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
PY - 1982
PB - Scuola normale superiore
VL - 9
IS - 4
SP - 529
EP - 570
LA - eng
KW - strictly pseudoconvex domain; Levi-flat hypersurface; stability theorem; polynomial hull
UR - http://eudml.org/doc/83891
ER -

References

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  1. [1] H. Alexander, Hulls of deformations in Cn, Trans. Amer. Math. Soc., 266 (1981), pp. 243-257. Zbl0493.32017MR613794
  2. [2] E. Bedford, Stability of the polynomial hull of T2, Ann. Scuola Norm. Sup. Pisa, 8 (1981), pp. 311-315. Zbl0472.32012MR623939
  3. [3] E. Bedford - P. De Bartolomeis, Levi flat hypersurfaces that are not holomorphically flat, Proc. Amer. Math. Soc., 81 (1981), pp. 575-578. Zbl0459.32007MR601733
  4. [4] E. Bedford - B. Gaveau, Envelopes of holomorphy of certain 2-spheres in C2, Amer. J. Math.. Zbl0535.32008
  5. [5] E. Bedford - B. Gaveau, Hypersurfaces with bounded Levi form, Indiana Univ. Math. J., 27 (1978), pp. 867-873. Zbl0365.32011MR499287
  6. [6] E. Bedford - B.A. Taylor, The Dirichlet problem for a complex Monge-Ampère equation, Invent. Math., 37 (1976), pp. 1-44. Zbl0315.31007MR445006
  7. [7] E. Bishop, Differentiable manifolds in complex Euclidean space, Duke Math. J., 32 (1965), pp. 1-22. Zbl0154.08501MR200476
  8. [8] A. Debiard - B. Gaveau, Problème de Dirichlet pour l'équation de Lévi, Bull. Sci. Math., 102 (1978), pp. 369-386. Zbl0411.35015MR517769
  9. [9] F. Docquier - H. Grauert, Levishes Problem und Rungescher Satz für Teilgebiete Steinscher Mannigfaltigkeiten, Math. Ann., 140 (1960), pp. 94-123. Zbl0095.28004MR148939
  10. [10] B. Gaveau, Méthodes de contrôle optimal en analyse complexe. - I: Résolution d'équations de Monge-Ampère, J. Functional Analysis, 25 (1977), pp. 391-411. Zbl0356.35071MR457783
  11. [11] C.D. Hill - G. Taiani, Families of analytic disks in Cn with boundaries in a prescribed CR submanifold, Ann. Scuola Norm. Sup. Pisa, 5 (1978), pp. 327-380. Zbl0399.32008MR501906
  12. [12] D. Kinderlehrer - L. Nirenberg, Regularity in free boundary problems, Ann. Scuola Norm. Sup. Pisa, 2 (1977), pp. 373-391. Zbl0352.35023MR440187
  13. [13] D. Kinderlehrer - G. Stampacchia, An Introduction to Variational Inequalities and their Applications, Academic Press, New York, 1980. Zbl0457.35001MR567696
  14. [14] R.S. Lehman, Development of the mapping function at an analytic corner, Pacific J. Math., 7 (1957), pp. 1437-1449. Zbl0087.28902MR95259
  15. [15] H. Lewy, The nature of the domain governed by different regimes, Atti del Convegno Internazionale Metodi valutativi nella hsicamatematica, Accad. Naz. Lincei (1975), pp. 181-188. 
  16. [16] J. Milnor,, Morse Theory, Princeton U. Press, 1963. Zbl0108.10401MR163331

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