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Plurisubharmonic saddles

100%

Momm S.

Annales Polonici Mathematici

1996

tom 63

nr 3

235-245

A certain linear growth of the pluricomplex Green function of a bounded convex domain of $ℂ^N$ at a given boundary point is related to the existence of a certain plurisubharmonic function called a "plurisubharmonic saddle". In view of classical results on the existence of angular derivatives of conformal mappings, for the case of a single complex variable, this allows us to deduce a criterion for the existence of subharmonic saddles.

On the multivariate transfinite diameter

88%

Bloom T. , Calvi J.-P.

Annales Polonici Mathematici

1999

tom 72

nr 3

285-305

We prove several new results on the multivariate transfinite diameter and its connection with pluripotential theory: a formula for the transfinite diameter of a general product set, a comparison theorem and a new expression involving Robin's functions. We also study the transfinite diameter of the pre-image under certain proper polynomial mappings.

Hoelder continuity property of composite Julia sets

51%

Kosek M.

Bulletin of the Polish Academy of Sciences. Mathematics

1998

tom Vol. 46, no 4

391--399

In this paper we consider the composite Julia associated with a finite family of the proper polynomial mappings in [C^n]. We show its pluricomplex Green function is Hoelder continous. This yields in particular that the set preserves Markov's inequality.