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## Annales Polonici Mathematici

1999 | 72 | 2 | 159-179
Tytuł artykułu

### A radial Phragmén-Lindelöf estimate for plurisubharmonic functions on algebraic varieties

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
For complex algebraic varieties V, the strong radial Phragmén-Lindelöf condition (SRPL) is defined. It means that a radial analogue of the classical Phragmén-Lindelöf Theorem holds on V. Here we derive a sufficient condition for V to satisfy (SRPL), which is formulated in terms of local hyperbolicity at infinite points of V. The latter condition as well as the extension of local hyperbolicity to varieties of arbitrary codimension are introduced here for the first time. The proof of the main result is based on a local version of the inequality of Sibony and Wong. The property (SRPL) provides a priori} estimates which can be used to deduce more refined Phragmén-Lindelöf results for algebraic varieties.
Słowa kluczowe
EN
Czasopismo
Rocznik
Tom
Numer
Strony
159-179
Opis fizyczny
Daty
wydano
1999
otrzymano
1998-11-19
poprawiono
1999-05-06
Twórcy
autor
• Mathematisches Institut, Heinrich-Heine-Universität, Universitätsstraße 1, 40225 Düsseldorf, Germany
autor
• Mathematisches Institut, Heinrich-Heine-Universität, Universitätsstraße 1, 40225 Düsseldorf, Germany
autor
• Department of Mathematics, University of Michigan, Ann Arbor, MI 48109, U.S.A.
Bibliografia
• [1] K. G. Andersson, Propagation of analyticity of solutions of partial differential equations with constant coefficients, Ark. Mat. 8 (1971), 277-302.
• [2] D. Bainbridge, Phragmén-Lindelöf estimates for plurisubharmonic functions of linear growth, thesis, Ann Arbor, 1998.
• [3] R. W. Braun, R. Meise and B. A. Taylor, An example concerning radial Phragmén-Lindelöf estimates for plurisubharmonic functions on algebraic varieties, Linear Topol. Spaces Complex Anal. 3 (1997), 24-29.
• [4] R. W. Braun, R. Meise and B. A. Taylor, A perturbation result for linear differential operators admitting a global right inverse on D', Pacific J. Math., to appear.
• [5] R. W. Braun, R. Meise and B. A. Taylor, Algebraic varieties on which the classical Phragmén-Lindelöf estimates hold for plurisubharmonic functions, Math. Z., to appear.
• [6] E. M. Chirka, Complex Analytic Sets, Kluwer, Dordrecht, 1989.
• [7] L. Hörmander, On the existence of real analytic solutions of partial differential equations with constant coefficients, Invent. Math. 21 (1973), 151-183.
• [8] R. Meise and B. A. Taylor, Phragmén-Lindelöf conditions for graph varieties, Results Math. 36 (1999), 121-148.
• [9] R. Meise, B. A. Taylor and D. Vogt, Characterization of the linear partial operators with constant coefficients that admit a continuous linear right inverse, Ann. Inst. Fourier (Grenoble) 40 (1990), 619-655.
• [10] R. Meise, B. A. Taylor and D. Vogt, Extremal plurisubharmonic functions of linear growth on algebraic varieties, Math. Z. 219 (1995), 515-537.
• [11] R. Meise, B. A. Taylor and D. Vogt, Continuous linear right inverses for partial differential operators on non-quasianalytic classes and on ultradistributions, Math. Nachr. 180 (1996), 213-242.
• [12] R. Meise, B. A. Taylor and D. Vogt, Phragmén-Lindelöf principles on algebraic varieties, J. Amer. Math. Soc. 11 (1998), 1-39.
• [13] D. Mumford, Algebraic Geometry I, Complex Projective Varieties, Grundlehren Math. Wiss. 221, Springer, Berlin, 1976.
• [14] N R. Nevanlinna, Eindeutige analytische Funktionen, Springer, 1974.
• [15] V. P. Palamodov, A criterion for splitness of differential complexes with constant coefficients, in: Geometrical and Algebraical Aspects in Several Complex Variables, C. A. Berenstein and D. C. Struppa (eds.), EditEL, 1991, 265-291.
• [16] I. R. Shafarevich, Basic Algebraic Geometry 1, Springer, 1994.
• [17] N. Sibony and P. Wong, Some results on global analytic sets, in: Séminaire Lelong-Skoda (Analyse), Lecture Notes in Math. 822, Springer, 1978-79, 221-237.
• [18] J. Siciak, Extremal plurisubharmonic functions in $ℂ^n$, Ann. Polon. Math. 39 (1981), 175-211.
• [19] J. Siciak, Extremal Plurisubharmonic Functions and Capacities in $ℂ^n$, Sophia Kokyuroku in Mathematics 14, Tokyo, 1982.
• [20] J. Stutz, Analytic sets as branched coverings, Trans. Amer. Math. Soc. 166 (1972), 241-259.
• [21] H. Whitney, Complex Analytic Varieties, Addison-Wesley, 1972.
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Bibliografia
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