Volume 54

2017

Publication date: 24.11.2017

Licence: CC BY-NC-ND

Editorial team

Editor-in-Chief Sławomir Kołodziej

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On the complex Monge-Ampère operator in unbounded domains

Per Åhag, Rafał Czyż

Universitatis Iagellonicae Acta Mathematica, Volume 54, 2017, pp. 7-13

https://doi.org/10.4467/20843828AM.17.001.7077

In this note we give sufficient conditions on a measure µ, defined on a unbounded strictly hyperconvex domain in Cⁿ, to be the MongeAmpere measure of some plurisubharmonic function. These generalize recent results by Le et al.

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Study of solutions of logarithmic order to higher order linear differential-difference equations with coeffcients having the same logarithmic order

Benharrat Belaïdi

Universitatis Iagellonicae Acta Mathematica, Volume 54, 2017, pp. 15-32

https://doi.org/10.4467/20843828AM.17.002.7078

The main purpose of this paper is to study the growth of solutions of the linear differential-difference equation L(z, f)= ⁿ ∑ _i=0 ^m ∑_j=0A_ij (z) f_(j)(z + c_i)=0, where Aij (z) (i = 0, ททท, n; j = 0, ททท, m) are entire or meromorphic functions of finite logarithmic order and ci (0, ททท, n) are distinct complex numbers. We extend some precedent results due to Wu and Zheng and others.

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A c-holomorphic effective Nullstellensatz with parameter

Maciej Denkowski

Universitatis Iagellonicae Acta Mathematica, Volume 54, 2017, pp. 33-41

https://doi.org/10.4467/20843828AM.17.003.7079

We prove a local Nullstellensatz with parameter for a continuous family of c-holomorphic functions with an effective exponent independent of the parameter: the local degree of the cycle of zeroes of the central section. We assume that this central section defines a proper intersection and we show that we can omit this assumption in case of isolated zeroes.

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On some factorial properties of subrings

Piotr Jędrzejewicz, Łukasz Matysiak, Janusz Zieliński

Universitatis Iagellonicae Acta Mathematica, Volume 54, 2017, pp. 43-52

https://doi.org/10.4467/20843828AM.17.004.7080

We discuss various factorial properties of subrings as well as properties involving irreducible elements and square-free elements, in particular ones connected with Jacobian conditions.

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Collapsing of Calabi-Yau manifolds and special Lagrangian submanifolds

Yuguang Zhang

Universitatis Iagellonicae Acta Mathematica, Volume 54, 2017, pp. 53-78

https://doi.org/10.4467/20843828AM.17.005.7081

In this paper, the relationship between the existence of special Lagrangian submanifolds and the collapsing of Calabi–Yau manifolds is studied. First, special Lagrangian fibrations are constructed on some regions of bounded curvature and sufficiently collapsed in Ricci-flat Calabi–Yau manifolds. Then, conversely, it is shown that the existence of special Lagrangian submanifolds with small volume implies the collapsing of some regions in the ambient Calabi–Yau manifolds.

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Słowa kluczowe: CComplex Monge-Amp±re operator, plurisubharmonic function, Dirichlet problem, unbounded hyperconvex domain., Linear differential-difference equation, meromorphic function, logarithmic order, logarithmic type, logarithmic lower order, logarithmic lower type., Nullstellensatz, c-holomorphic functions, Jacobian Conjecture, Irreducible element, square-free element, factorization

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