Generically strongly q -convex complex manifolds

Terrence Napier[1]; Mohan Ramachandran[2]

  • [1] Lehigh University, Department of Mathematics, Bethlehem PA 18015 (USA)
  • [2] SUNY at Buffalo, Department of Mathematics, Buffalo NY 14214 (USA)

Annales de l’institut Fourier (2001)

  • Volume: 51, Issue: 6, page 1553-1598
  • ISSN: 0373-0956

Abstract

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Suppose ϕ is a real analytic plurisubharmonic exhaustion function on a connected noncompact complex manifold X . The main result is that if the real analytic set of points at which ϕ is not strongly q -convex is of dimension at most 2 q + 1 , then almost every sufficiently large sublevel of ϕ is strongly q -convex as a complex manifold. For X of dimension 2 , this is a special case of a theorem of Diederich and Ohsawa. A version for ϕ real analytic with corners is also obtained.

How to cite

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Napier, Terrence, and Ramachandran, Mohan. "Generically strongly $q$-convex complex manifolds." Annales de l’institut Fourier 51.6 (2001): 1553-1598. <http://eudml.org/doc/115959>.

@article{Napier2001,
abstract = {Suppose $\varphi $ is a real analytic plurisubharmonic exhaustion function on a connected noncompact complex manifold $X$. The main result is that if the real analytic set of points at which $\varphi $ is not strongly $q$-convex is of dimension at most $2q+1$, then almost every sufficiently large sublevel of $\varphi $ is strongly $q$-convex as a complex manifold. For $X$ of dimension $2$, this is a special case of a theorem of Diederich and Ohsawa. A version for $\varphi $ real analytic with corners is also obtained.},
affiliation = {Lehigh University, Department of Mathematics, Bethlehem PA 18015 (USA); SUNY at Buffalo, Department of Mathematics, Buffalo NY 14214 (USA)},
author = {Napier, Terrence, Ramachandran, Mohan},
journal = {Annales de l’institut Fourier},
keywords = {analytic cycles; holomorphically convex; $q$-complete; -convexity; -complete},
language = {eng},
number = {6},
pages = {1553-1598},
publisher = {Association des Annales de l'Institut Fourier},
title = {Generically strongly $q$-convex complex manifolds},
url = {http://eudml.org/doc/115959},
volume = {51},
year = {2001},
}

TY - JOUR
AU - Napier, Terrence
AU - Ramachandran, Mohan
TI - Generically strongly $q$-convex complex manifolds
JO - Annales de l’institut Fourier
PY - 2001
PB - Association des Annales de l'Institut Fourier
VL - 51
IS - 6
SP - 1553
EP - 1598
AB - Suppose $\varphi $ is a real analytic plurisubharmonic exhaustion function on a connected noncompact complex manifold $X$. The main result is that if the real analytic set of points at which $\varphi $ is not strongly $q$-convex is of dimension at most $2q+1$, then almost every sufficiently large sublevel of $\varphi $ is strongly $q$-convex as a complex manifold. For $X$ of dimension $2$, this is a special case of a theorem of Diederich and Ohsawa. A version for $\varphi $ real analytic with corners is also obtained.
LA - eng
KW - analytic cycles; holomorphically convex; $q$-complete; -convexity; -complete
UR - http://eudml.org/doc/115959
ER -

References

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