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

Abstract

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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.

How to cite

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Braun, 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

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  1. [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. [2] D. Bainbridge, Phragmén-Lindelöf estimates for plurisubharmonic functions of linear growth, thesis, Ann Arbor, 1998. 
  3. [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. [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. [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. [6] E. M. Chirka, Complex Analytic Sets, Kluwer, Dordrecht, 1989. 
  7. [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. [8] R. Meise and B. A. Taylor, Phragmén-Lindelöf conditions for graph varieties, Results Math. 36 (1999), 121-148. Zbl0941.32032
  9. [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. [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. [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. [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. [13] D. Mumford, Algebraic Geometry I, Complex Projective Varieties, Grundlehren Math. Wiss. 221, Springer, Berlin, 1976. Zbl0356.14002
  14. [14] N R. Nevanlinna, Eindeutige analytische Funktionen, Springer, 1974. 
  15. [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. [16] I. R. Shafarevich, Basic Algebraic Geometry 1, Springer, 1994. Zbl0797.14001
  17. [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. [18] J. Siciak, Extremal plurisubharmonic functions in ℂ n , Ann. Polon. Math. 39 (1981), 175-211. Zbl0477.32018
  19. [19] J. Siciak, Extremal Plurisubharmonic Functions and Capacities in ℂ n , Sophia Kokyuroku in Mathematics 14, Tokyo, 1982. Zbl0579.32025
  20. [20] J. Stutz, Analytic sets as branched coverings, Trans. Amer. Math. Soc. 166 (1972), 241-259. Zbl0239.32006
  21. [21] H. Whitney, Complex Analytic Varieties, Addison-Wesley, 1972. Zbl0265.32008

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