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

Rüdiger Braun; Reinhold Meise; B. Taylor

Annales Polonici Mathematici (1999)

- Volume: 72, Issue: 2, page 159-179
- ISSN: 0066-2216

## Access Full Article

top## Abstract

top## How to cite

topBraun, Rüdiger, Meise, Reinhold, and Taylor, B.. "A radial Phragmén-Lindelöf estimate for plurisubharmonic functions on algebraic varieties." Annales Polonici Mathematici 72.2 (1999): 159-179. <http://eudml.org/doc/262783>.

@article{Braun1999,

abstract = {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.},

author = {Braun, Rüdiger, Meise, Reinhold, Taylor, B.},

journal = {Annales Polonici Mathematici},

keywords = {Phragmén-Lindelöf principle; Sibony-Wong inequality; Phragmén-Lindelöf principles},

language = {eng},

number = {2},

pages = {159-179},

title = {A radial Phragmén-Lindelöf estimate for plurisubharmonic functions on algebraic varieties},

url = {http://eudml.org/doc/262783},

volume = {72},

year = {1999},

}

TY - JOUR

AU - Braun, Rüdiger

AU - Meise, Reinhold

AU - Taylor, B.

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

JO - Annales Polonici Mathematici

PY - 1999

VL - 72

IS - 2

SP - 159

EP - 179

AB - 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.

LA - eng

KW - Phragmén-Lindelöf principle; Sibony-Wong inequality; Phragmén-Lindelöf principles

UR - http://eudml.org/doc/262783

ER -

## References

top- [1] K. G. Andersson, Propagation of analyticity of solutions of partial differential equations with constant coefficients, Ark. Mat. 8 (1971), 277-302. Zbl0211.40502
- [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. Zbl0926.32038
- [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. Zbl0963.35038
- [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. Zbl0933.32047
- [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. Zbl0282.35015
- [8] R. Meise and B. A. Taylor, Phragmén-Lindelöf conditions for graph varieties, Results Math. 36 (1999), 121-148. Zbl0941.32032
- [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. Zbl0703.46025
- [10] R. Meise, B. A. Taylor and D. Vogt, Extremal plurisubharmonic functions of linear growth on algebraic varieties, Math. Z. 219 (1995), 515-537. Zbl0835.32008
- [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. Zbl0858.46030
- [12] R. Meise, B. A. Taylor and D. Vogt, Phragmén-Lindelöf principles on algebraic varieties, J. Amer. Math. Soc. 11 (1998), 1-39. Zbl0896.32008
- [13] D. Mumford, Algebraic Geometry I, Complex Projective Varieties, Grundlehren Math. Wiss. 221, Springer, Berlin, 1976. Zbl0356.14002
- [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. Zbl1112.58304
- [16] I. R. Shafarevich, Basic Algebraic Geometry 1, Springer, 1994. Zbl0797.14001
- [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 ${\u2102}^{n}$, Ann. Polon. Math. 39 (1981), 175-211. Zbl0477.32018
- [19] J. Siciak, Extremal Plurisubharmonic Functions and Capacities in ${\u2102}^{n}$, Sophia Kokyuroku in Mathematics 14, Tokyo, 1982. Zbl0579.32025
- [20] J. Stutz, Analytic sets as branched coverings, Trans. Amer. Math. Soc. 166 (1972), 241-259. Zbl0239.32006
- [21] H. Whitney, Complex Analytic Varieties, Addison-Wesley, 1972. Zbl0265.32008

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.