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.
@article{bwmeta1.element.bwnjournal-article-apmv72z2p159bwm, author = {Braun, R\"udiger and Meise, Reinhold and Taylor, B.}, title = {A radial Phragm\'en-Lindel\"of estimate for plurisubharmonic functions on algebraic varieties}, journal = {Annales Polonici Mathematici}, volume = {72}, year = {1999}, pages = {159-179}, zbl = {0956.32030}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-apmv72z2p159bwm} }
Braun, Rüdiger; Meise, Reinhold; Taylor, B. A radial Phragmén-Lindelöf estimate for plurisubharmonic functions on algebraic varieties. Annales Polonici Mathematici, Tome 72 (1999) pp. 159-179. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-apmv72z2p159bwm/
[000] [1] K. G. Andersson, Propagation of analyticity of solutions of partial differential equations with constant coefficients, Ark. Mat. 8 (1971), 277-302. | Zbl 0211.40502
[001] [2] D. Bainbridge, Phragmén-Lindelöf estimates for plurisubharmonic functions of linear growth, thesis, Ann Arbor, 1998.
[002] [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. | Zbl 0926.32038
[003] [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. | Zbl 0963.35038
[004] [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. | Zbl 0933.32047
[005] [6] E. M. Chirka, Complex Analytic Sets, Kluwer, Dordrecht, 1989.
[006] [7] L. Hörmander, On the existence of real analytic solutions of partial differential equations with constant coefficients, Invent. Math. 21 (1973), 151-183. | Zbl 0282.35015
[007] [8] R. Meise and B. A. Taylor, Phragmén-Lindelöf conditions for graph varieties, Results Math. 36 (1999), 121-148. | Zbl 0941.32032
[008] [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. | Zbl 0703.46025
[009] [10] R. Meise, B. A. Taylor and D. Vogt, Extremal plurisubharmonic functions of linear growth on algebraic varieties, Math. Z. 219 (1995), 515-537. | Zbl 0835.32008
[010] [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. | Zbl 0858.46030
[011] [12] R. Meise, B. A. Taylor and D. Vogt, Phragmén-Lindelöf principles on algebraic varieties, J. Amer. Math. Soc. 11 (1998), 1-39. | Zbl 0896.32008
[012] [13] D. Mumford, Algebraic Geometry I, Complex Projective Varieties, Grundlehren Math. Wiss. 221, Springer, Berlin, 1976. | Zbl 0356.14002
[013] [14] N R. Nevanlinna, Eindeutige analytische Funktionen, Springer, 1974.
[014] [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. | Zbl 1112.58304
[015] [16] I. R. Shafarevich, Basic Algebraic Geometry 1, Springer, 1994. | Zbl 0797.14001
[016] [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.
[017] [18] J. Siciak, Extremal plurisubharmonic functions in , Ann. Polon. Math. 39 (1981), 175-211. | Zbl 0477.32018
[018] [19] J. Siciak, Extremal Plurisubharmonic Functions and Capacities in , Sophia Kokyuroku in Mathematics 14, Tokyo, 1982. | Zbl 0579.32025
[019] [20] J. Stutz, Analytic sets as branched coverings, Trans. Amer. Math. Soc. 166 (1972), 241-259. | Zbl 0239.32006
[020] [21] H. Whitney, Complex Analytic Varieties, Addison-Wesley, 1972. | Zbl 0265.32008