A microlocal version of Cartan-Grauert's theorem

I. V. Maresin; A. G. Sergeev

Annales Polonici Mathematici (1998)

  • Volume: 70, Issue: 1, page 157-162
  • ISSN: 0066-2216

Abstract

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Tuboids are tube-like domains which have a totally real edge and look asymptotically near the edge as a local tube over a convex cone. For such domains we state an analogue of Cartan’s theorem on the holomorphic convexity of totally real domains in ℝ n ⊂ ℂ n .

How to cite

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I. V. Maresin, and A. G. Sergeev. "A microlocal version of Cartan-Grauert's theorem." Annales Polonici Mathematici 70.1 (1998): 157-162. <http://eudml.org/doc/262864>.

@article{I1998,
abstract = {Tuboids are tube-like domains which have a totally real edge and look asymptotically near the edge as a local tube over a convex cone. For such domains we state an analogue of Cartan’s theorem on the holomorphic convexity of totally real domains in $ℝ^n ⊂ ℂ^n$.},
author = {I. V. Maresin, A. G. Sergeev},
journal = {Annales Polonici Mathematici},
keywords = {totally real submanifolds; domains of holomorphy; tuboids},
language = {eng},
number = {1},
pages = {157-162},
title = {A microlocal version of Cartan-Grauert's theorem},
url = {http://eudml.org/doc/262864},
volume = {70},
year = {1998},
}

TY - JOUR
AU - I. V. Maresin
AU - A. G. Sergeev
TI - A microlocal version of Cartan-Grauert's theorem
JO - Annales Polonici Mathematici
PY - 1998
VL - 70
IS - 1
SP - 157
EP - 162
AB - Tuboids are tube-like domains which have a totally real edge and look asymptotically near the edge as a local tube over a convex cone. For such domains we state an analogue of Cartan’s theorem on the holomorphic convexity of totally real domains in $ℝ^n ⊂ ℂ^n$.
LA - eng
KW - totally real submanifolds; domains of holomorphy; tuboids
UR - http://eudml.org/doc/262864
ER -

References

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  1. [1] J. Bros and D. Iagolnitzer, Tuboïdes et structure analytique des distributions, Sém. Goulaouic-Lions-Schwartz, nos. 16, 18, 1975. Zbl0333.46028
  2. [2] J. Bros and D. Iagolnitzer, Tuboïdes dans ℂ n et généralisation d’un théorème de Grauert, Ann. Inst. Fourier (Grenoble) 26 (1976), no. 3, 49-72. Zbl0336.32003
  3. [3] H. Cartan, Variétés analytiques réelles et variétés analytiques complexes, Bull. Soc. Math. France 85 (1957), 77-100. Zbl0083.30502
  4. [4] H. Grauert, On Levi's problem and the embedding of real analytic manifolds, Ann. of Math. (2) 68 (1958), 460-472. Zbl0108.07804
  5. [5] I. V. Maresin, Cartan-Grauert's theorem for tuboids with a curvilinear edge, Math. Notes 64 (1998), no. 6. Zbl0952.32001

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