Abstract
We discuss some results concerning local hyperconvexity and local hyperconcavity. In the convex case we show that a relatively compact locally hyperconvex open subset D of a complex space X is Stein if there exists a continuous strongly plurisubharmonic function in a neighbourhood of \(\overline D \). In the concave case we study the complement of a complete locally pluripolar set A ⊂ X. If X is Stein we show that A is complete globally pluripolar. A similar result is given for q-complete X. In this case A = ψ = − ∞ with ψ smooth and strongly q-convex outside A. As an application we study the neighbourhoods of complete locally pluripolar sets.
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© 1991 Friedr. Vieweg & Sohn Verlagsgesellschaft mbH, Braunschweig
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Colţoiu, M. (1991). Local hyperconvexity and local hyperconcavity. In: Diederich, K. (eds) Complex Analysis. Aspects of Mathematics, vol 1. Vieweg+Teubner Verlag. https://doi.org/10.1007/978-3-322-86856-5_15
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DOI: https://doi.org/10.1007/978-3-322-86856-5_15
Publisher Name: Vieweg+Teubner Verlag
Print ISBN: 978-3-322-86858-9
Online ISBN: 978-3-322-86856-5
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