A Generalization of the Annulus Formula for the Relative Extremal Function

Lewandowski, Arkadiusz

doi:10.7146/math.scand.a-18003

MATH. SCAND.

2014

DOI: 10.7146/math.scand.a-18003

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A Generalization of the Annulus Formula for the Relative Extremal Function

Arkadiusz Lewandowski¹

Abstract: The main result of this paper is an annulus formula for the relative extremal function in the context of Stein spaces (Theorem 1.1). It has an application in the theory of extensions of holomorphic functions defined on generalized crosses in products of Stein spaces (Theorem 4.6).

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A New Hartogs-Type Extension Result for the Cross-Like Objects

Lewandowski

2015

Kyushu J. Math.

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Abstract. We discuss the problem of the existence of envelopes of holomorphy of the new cross-type objects, the A -crosses, which leads us to the far-reaching generalizations of the famous Hartogs theorem. We also take under consideration the issue of the existence of 'nice' general descriptions of envelopes of holomorphy of the cross-like objects in terms of the relative extremal function, which seems to be very natural in the light of the extension theory of separately holomorphic functions on classical crosses and (N, k)-crosses.

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A New Hartogs-Type Extension Result for the Cross-Like Objects

Lewandowski

2015

Kyushu J. Math.

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A Generalization of the Annulus Formula for the Relative Extremal Function

Abstract: The main result of this paper is an annulus formula for the relative extremal function in the context of Stein spaces (Theorem 1.1). It has an application in the theory of extensions of holomorphic functions defined on generalized crosses in products of Stein spaces (Theorem 4.6).

Cited by 1 publication

References 18 publications

A New Hartogs-Type Extension Result for the Cross-Like Objects

A New Hartogs-Type Extension Result for the Cross-Like Objects

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