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1
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Invariant functions and metrics in complex analysis

100%
Nikolov N.
Instytut Matematyczny Polskiej Akademii Nauk
2
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Two remarks on the Suita conjecture

96%
Nikolov N.
Annales Polonici Mathematici
|
2015
|
tom 113
|
nr 1
61-63
EN
It is shown that the weak multidimensional Suita conjecture fails for any bounded non-pseudoconvex domain with $C^{1+ε}$-smooth boundary. On the other hand, it is proved that the weak converse to the Suita conjecture holds for any finitely connected planar domain.
3
Content available remote

The symmetrized polydisc cannot be exhausted by domains biholomorphic to convex domains

96%
Nikolov N.
Annales Polonici Mathematici
|
2006
|
tom 88
|
nr 3
279-283
EN
We prove that the symmetrized polydisc cannot be exhausted by domains biholomorphic to convex domains.
4
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Estimates for the Bergman kernel and metric of convex domains in ℂⁿ

61%
Nikolov N., Pflug P.
Annales Polonici Mathematici
|
2003
|
tom 81
|
nr 1
73-78
EN
Sharp geometrical lower and upper estimates are obtained for the Bergman kernel on the diagonal of a convex domain D ⊂ ℂⁿ which does not contain complex lines. It is also proved that the ratio of the Bergman and Carathéodory metrics of D does not exceed a constant depending only on n.
5
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Concave domains with trivial biholomorphic invariants

61%
Jarnicki W., Nikolov N.
Annales Polonici Mathematici
|
2002
|
tom 79
|
nr 1
63-66
EN
It is proved that if F is a convex closed set in ℂⁿ, n ≥2, containing at most one (n-1)-dimensional complex hyperplane, then the Kobayashi metric and the Lempert function of ℂⁿ∖ F identically vanish.
6
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On the zero set of the Kobayashi-Royden pseudometric of the spectral unit ball

61%
Nikolov N., Thomas P.
Annales Polonici Mathematici
|
2008
|
tom 93
|
nr 1
53-68
EN
Given A∈ Ωₙ, the n²-dimensional spectral unit ball, we show that if B is an n×n complex matrix, then B is a "generalized" tangent vector at A to an entire curve in Ωₙ if and only if B is in the tangent cone $C_A$ to the isospectral variety at A. In the case of Ω₃, the zero set of the Kobayashi-Royden pseudometric is completely described.
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