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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.

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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
\Bibitem{Tum88}
\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
\mathnet{http://mi.mathnet.ru/msb1732}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=945904}
\zmath{https://zbmath.org/?q=an:0692.58005}
\transl
\jour Math. USSR-Sb.
\yr 1989
\vol 64
\issue 1
\pages 129--140
\crossref{https://doi.org/10.1070/SM1989v064n01ABEH003298}


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    Citing articles on Google Scholar: Russian citations, English citations
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    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
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    41. Lahondes P., “Extensions of Cr Homeomorphisms Between Rigid Polynomial Varieties”, Publ. Mat., 46:2 (2002), 327–352  mathscinet  zmath  isi
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    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
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    51. Kojcinovic S., “Extension of Cr Mappings Between Generic Algebraic Submanifolds”, Pac. J. Math., 220:2 (2005), 359–378  crossref  mathscinet  zmath  isi
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    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
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    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
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    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)
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