Holomorphic extension from weakly pseudoconcave CR manifolds

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1. [AMN] A. Altomani - C. Medori - M. Nacinovich, The CR structure of minimal orbits in complex flag manifolds, J. Lie Theory, 16 (2006), pp. 483--530. Zbl1120.32023MR2248142
2. [BR] M. S. Baouendi - L. P. Rothschild, Cauchy Riemann functions on manifolds of higher codimension in complex space, Invent. Math., 101 (1990), pp. 45--56. Zbl0712.32009MR1055709
3. [BT1] 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. Zbl0491.35036MR607899
4. [BT2] M. S. Baouendi - F. Treves, About the holomorphic extension of CR functions on real hypersurfaces in complex space, Duke Math. J., 51, no. 1 (1984), pp. 77--107. Zbl0564.32011MR744289
5. [B] E. Bishop, Differentiable manifolds in complex Euclidean space, Duke Math. J., 32 (1965), pp. 1--21. Zbl0154.08501MR200476
6. [Bo] A. Boggess, CR extendability near a point where the first Levi form vanishes, Duke Math. J., 48 (1981), pp. 665--684. Zbl0509.32006MR630590
7. [BP] A. Boggess - J. Polking, Holomorphic extensions of $CR$ functions, Duke Math. J., 49 (1982), pp. 757--784. Zbl0506.32003MR683002
8. [DS] T. C. Dinh - F. Sarkis, Wedge removability of metrically thin sets and application to the CR meromorphic extension, Math. Z., 238 (2001), pp. 639--653. Zbl1002.32027MR1869700
9. [DH] P. Dolbeault - G. Henkin, Chaines holomorphes de bord donné dans un ouvert q-concave de $C{P}^n$, Bull. Soc. Math. France, 125 (1997), pp. 383--445. Zbl0942.32007MR1605457
10. [FR] J. E. Fornaess - C. Rea, Local holomorphic extendability and nonextendability of CR-functions on smooth boundaries, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4), 12, no. 3 (1985), pp. 491--502. Zbl0587.32035MR837258
11. [HL] R. Harvey - B. Lawson, On boundaries of complex analytic varieties, Part II, Ann. Math., 106 (1977), pp. 213--238. Zbl0361.32010MR499285
12. [HN1] C. D. Hill - M. Nacinovich, A weak pseudoconcavity condition for abstract almost CR manifolds, Invent. Math., 142 (2000), pp. 251--283. Zbl0973.32018MR1794063
13. [HN2] C. D. Hill - M. Nacinovich, Fields of CR meromorphic functions, Rend. Sem. Mat. Univ. Padova, 111 (2004), pp. 179--204. Zbl1121.32018MR2076739
14. [HN3] C. D. Hill - M. Nacinovich, Elementary pseudoconcavity and fields of CR meromorphic functions, Rend. Sem. Mat. Univ. Padova, 113 (2005), pp. 99--115. Zbl1167.32301MR2168982
15. [HN4] C. D. Hill - M. Nacinovich, Conormal suspensions of differential complexes, J. Geom. Anal., 10, 3 (2000), pp. 496--537. Zbl0989.58007MR1794574
16. [HT] C. D. Hill - G. Taiani, Families of analytic discs in ${ℂ}^n$ with boundaries on a prescribed CR submanifold, Ann. Sc. Norm. Pisa, 5 (1978), pp. 327--380. Zbl0399.32008MR501906
17. [J] B. Jöricke, Deformation of CR-manifolds, minimal points and CR-manifolds with the microlocal analytic extension property, J. Geom. Anal., 6 (1996), pp. 555--611. Zbl0917.32007MR1601405
18. [MN1] C. Medori - M. Nacinovich, Levi-Tanaka algebras and homogeneous CR manifolds, Compositio Mathematica, 109 (1997), pp. 195--250. Zbl0955.32029MR1478818
19. [MN2] C. Medori - M. Nacinovich, Classification of semisimple Levi-Tanaka algebras, Ann. Mat. Pura Appl., CLXXIV (1998), pp. 285--349. Zbl0999.17039MR1746933
20. [MN3] C. Medori - M. Nacinovich, Complete nondegenerate locally standard CR manifolds, Math. Ann., 317 (2000), pp. 509--526. Zbl1037.32031MR1776115
21. [MN4] C. Medori - M. Nacinovich, Algebras of infinitesimal CR automorphisms, J. Algebra, 287 (2005), pp. 234--274. Zbl1132.32013MR2134266
22. [M] J. Merker, Global minimality of generic manifolds and holomorphic extendibility of CR functions, IMRN, 8 (1994), pp. 329--342. Zbl0815.32007MR1289578
23. [MP1] J. Merker - E. Porten, On the local meromorphic extension of CR meromorphic mappings, Ann. Polon. Math., 70 (1998), pp. 163--193. Zbl0927.32024MR1668724
24. [MP2] J. Merker - E. Porten, Metrically thin singularities of integrable CR functions, Internat. J. Math., 11 (2000), pp. 857--872. Zbl0967.32010MR1792956
25. [MP3] J. Merker - E. Porten, Characteristic foliations on maximally real submanifolds of ${ℂ}^n$ and removable singularities for CR functions, IMRP, Volume 2006 (2006), Article ID 72069, pp.1--131. Zbl1122.32023MR2268488
26. [MP4] J. Merker - E. Porten, Holomorphic Extension of CR Functions, Envelopes of Holomorphy, and Removable Singularities, IMRS, Volume 2006 (2006), Article ID 28925, pp.1--286. Zbl1149.32019MR2270252
27. [NV] M. Nacinovich - G. Valli,Tangential Cauchy-Riemann complexes on distributions, Ann. Mat. Pura Appl., 146 (1987), pp. 123--160. Zbl0631.58024MR916690
28. [S] J. Sjöstrand, The FBI transform for CR submanifolds of ${ℂ}^n$, Prépublications Mathématiques Orsay 1982. 
29. [T1] J.-M. Trépreau, Sur le prolongement holomorphe des fonctions CR définies sur une hypersurface reelle de classe $C^2$, Invent. Math., 83 (1986), pp. 583--592. Zbl0586.32016MR827369
30. [T2] J.-M. Trépreau, Sur la propagation des singularités dans les variétés CR, Bull. Soc. Math. Fr., 118 (1990), pp. 403--450. Zbl0742.58053MR1090408
31. [T] F. Treves, Hypoanalytic Structures: Local Theory, Princeton Univ. Press 1992. Zbl0787.35003MR1200459
32. [Tu1] A. E. Tumanov, Extension of CR-functions into a wedge from a manifold of finite type, Math. USSR Sb., 64 (1989), pp. 129--140. Zbl0692.58005MR945904
33. [Tu2] A. E. Tumanov, On the propagation of extendability of CR functions, Complex Analysis and Geometry, Proc. of the Conference in Trento 1995. Lecture Notes in Pure and Appl. Math., 173 (Dekker 1996), pp. 479--498. Zbl0849.32013