The Levi problem on complex spaces with singularities

Fornæss, John Erik; Narasimhan, Raghavan

doi:10.1007/bf01349254

Cited by 163 publications

(83 citation statements)

References 15 publications

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“…Note that, although it is close to results in [4], it requires a careful analysis and for its proof we need the generalized Remmert reduction theorem due to Wiegmann [23].…”

Section: An Auxiliary Resultsmentioning

confidence: 81%

A cohomological steinness criterion for holomorphically spreadable complex spaces

Vâjâitu

2010

Czech Math J

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“…Note that, although it is close to results in [4], it requires a careful analysis and for its proof we need the generalized Remmert reduction theorem due to Wiegmann [23].…”

Section: An Auxiliary Resultsmentioning

confidence: 81%

A cohomological steinness criterion for holomorphically spreadable complex spaces

Vâjâitu

2010

Czech Math J

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“…The result is known in the case where φ is smooth; see [7]. In the general case, since Y is Stein we know from [5] that there is a sequence φ n of smooth strictly plurisubharmonic functions on Y pointwise decreasing to φ. By integration on the K orbits and using Dini theorem, we find a sequence of smooth strictly plurisubharmonic K invariant functions pointwise decreasing to φ.…”

Section: Examples 29 Every Stein Space Is Cmentioning

confidence: 97%

“…By [5], there exists a decreasing sequence τ n of smooth strictly plurisubharmonic functions which pointwise converge to τ on Ω ∩ (K C × U ). By averaging we may assume that each τ n is K invariant.…”

Section: Main Theoremmentioning

confidence: 99%

Torus actions on weakly pseudoconvex spaces

Trapani

2005

Trans. Amer. Math. Soc.

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“…By a deep result of Fornaess and Narasimhan [8], any weakly plurisubharmonic function is in fact strongly plurisubharmonic (this is also true in the more general setting of complex spaces), and we will make good use of this fact later on. On the other hand, almost plurisubharmonic functions do not necessarily extend to any neighborhood of the variety, as shown by the following example: Example 1.3.…”

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confidence: 93%

Continuity of the relative extremal function on analytic varieties in Cⁿ

Wikström

2005

Ann. Polon. Math.

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Abstract. Let V be an analytic variety in a domain Ω ⊂ C n and let K ⊂⊂ V be a closed subset. By studying Jensen measures for certain classes of plurisubharmonic functions on V , we prove that the relative extremal function ω K is continuous on V if Ω is hyperconvex and K is regular.1. Introduction. Let P (D) be a linear partial differential operator with constant coefficients. Hörmander [9] gave a characterization of when P (D) is surjective on the space A(Ω) of real-analytic functions when Ω is a convex domain in R n . This characterization is stated in terms of Phragmén-Lindelöf type estimates for plurisubharmonic functions on the zero variety of the symbol of P (D). Hörmander's result has been the main inspiration for trying to find various kinds of geometric or algebraic criteria for recognizing varieties satisfying such Phragmén-Lindelöf estimates, and there are a large number of papers attacking this problem. One of the tools that have been used is the relative extremal function ω K . (See for example [1,2,3].) The main goal of this paper is to prove that ω K is continuous if K is regular. To state the result more precisely, we will require some preliminary definitions.there is an open neighborhood U of x such that V ∩ U is irreducible, we say that V is locally irreducible at x. We denote by V irr the set of locally irreducible points in V . If x ∈ V irr , we say that V is reducible at x; we denote the set of reducible points by V red . Note that V irr is an open dense subset of V containing all regular points of V .

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The Levi problem on complex spaces with singularities

Cited by 163 publications

References 15 publications

A cohomological steinness criterion for holomorphically spreadable complex spaces

A cohomological steinness criterion for holomorphically spreadable complex spaces

Torus actions on weakly pseudoconvex spaces

Continuity of the relative extremal function on analytic varieties in Cⁿ

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The Levi problem on complex spaces with singularities

Cited by 163 publications

References 15 publications

A cohomological steinness criterion for holomorphically spreadable complex spaces

A cohomological steinness criterion for holomorphically spreadable complex spaces

Torus actions on weakly pseudoconvex spaces

Continuity of the relative extremal function on analytic varieties in Cn

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Continuity of the relative extremal function on analytic varieties in Cⁿ