General information
Latest issue
Forthcoming papers
Impact factor
Guidelines for authors
License agreement
Submit a manuscript

Search papers
Search references

Latest issue
Current issues
Archive issues
What is RSS

Mat. Sb.:

Personal entry:
Save password
Forgotten password?

Mat. Sb. (N.S.), 1988, Volume 136(178), Number 1(5), Pages 128–139 (Mi msb1732)  

This article is cited in 66 scientific papers (total in 66 papers)

Extension of $\mathrm{CR}$ functions into a wedge from a manifold of finite type

A. E. Tumanov

Abstract: It is shown that, if a generating manifold $M\in C^n$ does not contain proper submanifolds of the same $\mathrm{CR}$ dimension as $M$, then all $\mathrm{CR}$ functions can be extended from $M$ into some wedge with edge $M$. In particular, extension of all $\mathrm{CR}$ functions into a wedge necessarily obtains for manifolds of finite type.
Bibliography: 21 titles.

Full text: PDF file (659 kB)
References: PDF file   HTML file

English version:
Mathematics of the USSR-Sbornik, 1989, 64:1, 129–140

Bibliographic databases:

UDC: 517.55
MSC: Primary 32D15; Secondary 32A99
Received: 20.04.1987

Citation: A. E. Tumanov, “Extension of $\mathrm{CR}$ functions into a wedge from a manifold of finite type”, Mat. Sb. (N.S.), 136(178):1(5) (1988), 128–139; Math. USSR-Sb., 64:1 (1989), 129–140

Citation in format AMSBIB
\by A.~E.~Tumanov
\paper Extension of $\mathrm{CR}$ functions into a~wedge from a~manifold of finite type
\jour Mat. Sb. (N.S.)
\yr 1988
\vol 136(178)
\issue 1(5)
\pages 128--139
\jour Math. USSR-Sb.
\yr 1989
\vol 64
\issue 1
\pages 129--140

Linking options:

    SHARE: FaceBook Twitter Livejournal

    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. A. E. Tumanov, “Extension of CR-functions into a wedge”, Math. USSR-Sb., 70:2 (1991), 385–398  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    2. Trepreau J., “Propagation of Singularities in Cauchy-Riemann Manifolds”, Bull. Soc. Math. Fr., 118:4 (1990), 403–450  mathscinet  zmath  isi
    3. E. M. Chirka, “Introduction to the geometry of $CR$-manifolds”, Russian Math. Surveys, 46:1 (1991), 95–197  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    4. Dwilewicz R., Hill C., “An Analytic Disk Approach to the Notion of Type of Points”, Indiana Univ. Math. J., 41:3 (1992), 713–739  crossref  mathscinet  zmath  isi
    5. Dwilewicz R., Hill C., “A Characterization of Harmonic-Functions and Points of Finite and Infinite Type”, Indag. Math.-New Ser., 4:1 (1993), 39–50  crossref  mathscinet  zmath  isi
    6. Baouendi M., Rothschild L., “A Generalized Complex Hopf Lemma and its Applications to Cr Mappings”, Invent. Math., 111:2 (1993), 331–348  crossref  mathscinet  zmath  adsnasa  isi
    7. Hanges N., Treves F., “On the Local Holomorphic Extension of Cr Functions”, Asterisque, 1993, no. 217, 119–137  mathscinet  zmath  isi
    8. Meylan F., “Extension of Germs of Smooth Cr Diffeomorphisms Between Non Essentially Finite Hypersurfaces in C-3”, Comptes Rendus Acad. Sci. Ser. I-Math., 319:8 (1994), 827–830  mathscinet  zmath  isi
    9. Baouendi M., Rothschild L., “Directions of Analytic Disks Attached to Generic Manifolds of Finite-Type”, J. Funct. Anal., 125:1 (1994), 149–171  crossref  mathscinet  zmath  isi
    10. Baouendi M., Rothschild L., Trepreau J., “On the Geometry of Analytic Disks Attached to Real Manifolds”, J. Differ. Geom., 39:2 (1994), 379–405  mathscinet  zmath  isi
    11. Cerne M., “Analytic Discs Attached to a Generating Cr-Manifold”, Ark. Mat., 33:2 (1995), 217–248  crossref  mathscinet  zmath  isi
    12. Meylan F., “The Reflection Principle in Complex Space”, Indiana Univ. Math. J., 44:3 (1995), 783–796  crossref  mathscinet  zmath  isi
    13. Hill C., Nacinovich M., “The Jacobian-Theorem for Mapping of Pseudoconcave Cr Hypersurfaces”, Boll. Unione Mat. Italiana, 9A:1 (1995), 149–155  mathscinet  zmath  isi
    14. Eisen N., “Holomorphic Sections of a Vector Bundle and its Conormal Bundle Over the Circle”, Indiana Univ. Math. J., 45:3 (1996), 773–795  crossref  mathscinet  zmath  isi
    15. Huang X., Pan Y., “Proper Holomorphic Mappings Between Real Analytic Domains in C-N”, Duke Math. J., 82:2 (1996), 437–446  crossref  mathscinet  zmath  isi
    16. Pan Y., “A Characterization of the Finite Multiplicity of a Cr Mapping”, Mich. Math. J., 43:3 (1996), 465–474  crossref  mathscinet  zmath  isi
    17. Vityaev A., “On Extension of Cr Functions From Piecewise Smooth Manifolds Into a Wedge”, Ill. J. Math., 41:2 (1997), 193–213  mathscinet  zmath  isi
    18. Helton J., Vityaev A., “Analytic Functions Optimizing Competing Constraints”, SIAM J. Math. Anal., 28:3 (1997), 749–767  crossref  mathscinet  zmath  isi
    19. Merker J., “On Removable Singularities for Cr Functions in Higher Codimension”, Int. Math. Res. Notices, 1997, no. 1, 21–56  crossref  mathscinet  zmath  isi
    20. Cerne M., “Regularity of Discs Attached to a Submanifold of C-N”, J. Anal. Math., 72 (1997), 261–278  crossref  mathscinet  zmath  isi
    21. Dwilewicz R. Hill C., “Spinning Analytic Discs and Domains of Dependence”, Manuscr. Math., 97:4 (1998), 407–427  crossref  mathscinet  zmath  isi
    22. Hayashimoto A., “On the Complete System of Finite Order for Cr Mappings and its Application”, Osaka J. Math., 35:3 (1998), 617–628  mathscinet  zmath  isi
    23. Chirka E., Rea C., “Differentiable Cr Mappings and Cr Orbits”, Duke Math. J., 94:2 (1998), 325–340  crossref  mathscinet  zmath  isi
    24. Huang X., “On an N-Manifold in C-N Near an Elliptic Complex Tangent”, J. Am. Math. Soc., 11:3 (1998), 669–692  crossref  mathscinet  zmath  isi
    25. Boivin A., Dwilewicz R., “Extension and Approximation of Cr Functions on Tube Manifolds”, Trans. Am. Math. Soc., 350:5 (1998), 1945–1956  crossref  mathscinet  zmath  isi
    26. Mir N., “Germs of Holomorphic Mappings Between Real Algebraic Hypersurfaces”, Ann. Inst. Fourier, 48:4 (1998), 1025+  crossref  mathscinet  zmath  isi
    27. Dmitri Zaitsev, “Algebraicity of local holomorphisms between real-algebraic submanifolds of complex spaces”, Acta Math, 183:2 (1999), 273  crossref  mathscinet  zmath  isi
    28. Dwilewicz R., “Pseudoconvexity and Analytic Discs”, Ann. Glob. Anal. Geom., 17:6 (1999), 539–561  crossref  mathscinet  zmath  isi
    29. Merker J. Porten E., “On Removable Singularities for Integrable Cr Functions”, Indiana Univ. Math. J., 48:3 (1999), 805–856  crossref  mathscinet  zmath  isi
    30. K OELJEKLAUS, C SACRE, “Variétés Cauchy–Riemann homogènes et enveloppes holomorphes”, Bulletin des Sciences Mathématiques, 124:3 (2000), 193  crossref
    31. Wilhelm Kaup, Dmitri Zaitsev, “On Symmetric Cauchy–Riemann Manifolds”, Advances in Mathematics, 149:2 (2000), 145  crossref
    32. Hill C., Nacinovich M., “A Weak Pseudoconcavity Condition for Abstract Almost Cr Manifolds”, Invent. Math., 142:2 (2000), 251–283  crossref  mathscinet  zmath  adsnasa  isi
    33. Laurent-Thiebaut C., Leiterer J., “Malgrange's Vanishing Theorem in 1-Concave Cr Manifolds”, Nagoya Math. J., 157 (2000), 59–72  mathscinet  zmath  isi
    34. Ebenfelt P., Huang X., “On a Generalized Reflection Principle in C-2”, Complex Analysis and Geometry, Ohio State University Mathematical Research Institute Publications, 9, ed. McNeal J., Walter de Gruyter & Co, 2001, 125–140  mathscinet  isi
    35. Meylan F., Mir N., Zaitsev D., “Approximation and Convergence Properties of Formal Cr-Maps”, C. R. Math., 335:8 (2002), 671–676  crossref  mathscinet  zmath  isi
    36. Dwilewicz R. Hill C., “The Conormal Type Function for Cr Manifolds”, Publ. Math.-Debr., 60:3-4 (2002), 245–282  mathscinet  zmath  isi
    37. Ebenfelt P., “On the Analyticity of Cr Mappings Between Nonminimal Hypersurfaces”, Math. Ann., 322:3 (2002), 583–602  crossref  mathscinet  zmath  isi
    38. Merker J., “On Envelopes of Holomorphy of Domains Covered by Levi-Flat Hats and the Reflection Principle”, Ann. Inst. Fourier, 52:5 (2002), 1443+  crossref  mathscinet  zmath  isi
    39. Mir N., “On the Convergence of Formal Mappings”, Commun. Anal. Geom., 10:1 (2002), 23–59  mathscinet  zmath  isi
    40. Meylan F. Mir N. Zaitsev D., “Analytic Regularity of Cr-Mappings”, Math. Res. Lett., 9:1 (2002), 73–93  mathscinet  zmath  isi
    41. Lahondes P., “Extensions of Cr Homeomorphisms Between Rigid Polynomial Varieties”, Publ. Mat., 46:2 (2002), 327–352  mathscinet  zmath  isi
    42. Luca Baracco, “Analytic discs in conormal bundles to real submanifolds of ℂ n ”, Isr J Math, 137:1 (2003), 149  crossref  mathscinet  zmath  isi
    43. Kaup W., Zaitsev D., “On the Cr-Structure of Compact Group Orbits Associated with Bounded Symmetric Domains”, Invent. Math., 153:1 (2003), 45–104  crossref  mathscinet  zmath  adsnasa  isi
    44. Hayashimoto A., Kin S.-Y., Zaitsev D., “Decomposition of Cr-Manifolds and Splitting of Cr-Maps”, Ann. Scuola Norm. Super. Pisa-Cl. Sci., 2:3 (2003), 433–448  mathscinet  zmath  isi
    45. Merker J., “Propagation of Analyticity for Essentially Finite C-Infinity-Smooth Cr Mappings”, Manuscr. Math., 115:3 (2004), 313–338  crossref  mathscinet  zmath  isi
    46. Baouendi M., Rothschild L., Winkelmann J., Zaitsev D., “Lie Group Structures on Groups of Diffeomorphisms and Applications to Cr Manifolds”, Ann. Inst. Fourier, 54:5 (2004), 1279+  crossref  mathscinet  zmath  isi
    47. V. K. Beloshapka, “Universal Models For Real Submanifolds”, Math. Notes, 75:4 (2004), 475–488  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    48. Bernard Coupet, Alexandre Sukhov, “Reflection principle and boundary properties of holomorphic mappings”, Journal of Mathematical Sciences (New York), 125:6 (2005), 825  crossref  mathscinet  zmath  elib
    49. Nikolai Kruzhilin, Alexandre Sukhov, “Pseudoholomorphic discs attached to CR-submanifolds of almost complex spaces”, Bulletin des Sciences Mathématiques, 129:5 (2005), 398  crossref  elib
    50. Dolbeault P., Tomassini G., Zaitsev D., “On Boundaries of Levi-Flat Hypersurfaces in C-N”, C. R. Math., 341:6 (2005), 343–348  crossref  mathscinet  zmath  isi
    51. Kojcinovic S., “Extension of Cr Mappings Between Generic Algebraic Submanifolds”, Pac. J. Math., 220:2 (2005), 359–378  crossref  mathscinet  zmath  isi
    52. Chirka E., Rea C., “F. and M. Riesz Theorem for Cr Functions”, Math. Z., 250:1 (2005), 1–6  crossref  mathscinet  zmath  isi  elib
    53. Kaup W., Zaitsev D., “On Local Cr-Transformations of Levi-Degenerate Group Orbits in Compact Hermitian Symmetric Spaces”, J. Eur. Math. Soc., 8:3 (2006), 465–490  crossref  mathscinet  zmath  isi
    54. Lamal B., Mir N., Zaitsev D., “Lie Group Structures on Automorphism Groups of Real-Analytic Cr Manifolds”, Am. J. Math., 130:6 (2008), 1709–1726  crossref  mathscinet  isi
    55. Chang D.-Ch., Eby W., “Pompeiu Problem for Sets of Higher Codimension in Euclidean and Heisenberg Settings”, Taiwan. J. Math., 12:9 (2008), 2619–2640  mathscinet  zmath  isi
    56. Chakrabarti D. Shafikov R., “Holomorphic Extension of Cr Functions From Quadratic Cones”, Math. Ann., 341:3 (2008), 543–573  crossref  mathscinet  zmath  isi  elib
    57. Hui Ch.Y., “An Extension Result of Cr Functions by a General Schwarz Reflection Principle”, Complex Var. Elliptic Equ., 54:10 (2009), 927–934  crossref  mathscinet  zmath  isi
    58. Altomani A., Hill C.D., Nacinovich M., Porten E., “Holomorphic Extension From Weakly Pseudoconcave Cr Manifolds”, Rend. Semin. Mat. Univ. Padova, 123 (2010), 69–90  crossref  mathscinet  zmath  isi
    59. Małgorzata Aneta Marciniak, “Holomorphic Extensions in Smooth Toric Surfaces”, J Geom Anal, 22:4 (2011), 911  crossref
    60. Eisen N., “On the Holomorphic Extension of Cr Functions From Nongeneric Cr Submanifolds of C-N: the Positive Defect Case”, Mich. Math. J., 60:1 (2011), 149–162  crossref  mathscinet  isi
    61. Eisen N., “On the Holomorphic Extension of Cr Functions From Non-Generic Cr Submanifolds of C-N”, Ark. Mat., 50:1 (2012), 69–87  crossref  mathscinet  zmath  isi
    62. Hill C.D. Nacinovich M., “Non Completely Solvable Systems of Complex First Order PDE'S”, Rend. Semin. Mat. Univ. Padova, 129 (2013), 129–169  crossref  isi
    63. Florian Bertrand, Giuseppe Della Sala, “Stationary Discs for Smooth Hypersurfaces of Finite Type and Finite Jet Determination”, J Geom Anal, 2014  crossref
    64. Kossovskiy I. Lamel B., “New extension phenomena for solutions of tangential Cauchy–Riemann equations”, Commun. Partial Differ. Equ., 41:6 (2016), 925–951  crossref  mathscinet  zmath  isi  scopus
    65. Kossovskiy I., Shafikov R., “Divergent CR-equivalences and meromorphic differential equations”, J. Eur. Math. Soc., 18:12 (2016), 2785–2819  crossref  mathscinet  zmath  isi  scopus
    66. Kossovskiy I., Lamel B., “On the Analyticity of Cr-Diffeomorphisms”, Am. J. Math., 140:1 (2018), 139–188  crossref  isi
  • Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics (from 1967)
    Number of views:
    This page:260
    Full text:60

    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2019