PL EN


Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników
2000 | 75 | 3 | 213-231
Tytuł artykułu

Newton numbers and residual measures of plurisubharmonic functions

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We study the masses charged by $(dd^cu)^n$ at isolated singularity points of plurisubharmonic functions u. This is done by means of the local indicators of plurisubharmonic functions introduced in [15]. As a consequence, bounds for the masses are obtained in terms of the directional Lelong numbers of u, and the notion of the Newton number for a holomorphic mapping is extended to arbitrary plurisubharmonic functions. We also describe the local indicator of u as the logarithmic tangent to u.
Rocznik
Tom
75
Numer
3
Strony
213-231
Opis fizyczny
Daty
wydano
2000
otrzymano
1999-07-20
poprawiono
2000-04-04
Twórcy
  • Mathematical Division, Institute for Low Temperature Physics, 47 Lenin Ave., Kharkov 310164, Ukraine
Bibliografia
  • [1] L. A. Aĭzenberg and Yu. P. Yuzhakov, Integral Representations and Residues in Multidimensional Complex Analysis, Nauka, Novosibirsk, 1979 (in Russian); English transl.: AMS, Providence, RI, 1983.
  • [2] J.-P. Demailly, Monge-Ampère operators, Lelong numbers and intersection theory, in: Complex Analysis and Geometry, V. Ancona and A. Silva (eds.), Plenum Press, New York, 1993, 115-193.
  • [3] L. Hörmander, Notions of Convexity, Progr. Math. 127, Birkhäuser, 1994.
  • [4] C. O. Kiselman, Densité des fonctions plurisousharmoniques, Bull. Soc. Math. France 107 (1979), 295-304.
  • [5] C. O. Kiselman, Un nombre de Lelong raffiné, in: Séminaire d'Analyse Complexe et Géométrie 1985-87, Fac. Sci. Monastir, 1987, 61-70.
  • [6] C. O. Kiselman, Tangents of plurisubharmonic functions, in: International Symposium in Memory of Hua Loo Keng, Vol. II, Science Press and Springer, 1991, 157-167.
  • [7] C. O. Kiselman, Attenuating the singularities of plurisubharmonic functions, Ann. Polon. Math. 60 (1994), 173-197.
  • [8] M. Klimek, Pluripotential Theory, Oxford Univ. Press, London, 1991.
  • [9] A. G. Kouchnirenko, Newton polyhedron and the number of solutions of a system of k equations with k indeterminates, Uspekhi Mat. Nauk 30 (1975), no. 2, 266-267 (in Russian).
  • [10] A. G. Kouchnirenko, Polyèdres de Newton et nombres de Milnor, Invent. Math. 32 (1976), 1-31.
  • [11] S. Lang, Fundamentals of Diophantine Geometry, Springer, New York, 1983.
  • [12] P. Lelong, Plurisubharmonic Functions and Positive Differential Forms, Gordon and Breach, New York, and Dunod, Paris, 1969.
  • [13] P. Lelong, Remarks on pointwise multiplicities, Linear Topol. Spaces Complex Anal. 3 (1997), 112-119.
  • [14] P. Lelong and L. Gruman, Entire Functions of Several Complex Variables, Springer, Berlin, 1986.
  • [15] P. Lelong and A. Rashkovskii, Local indicators for plurisubharmonic functions, J. Math. Pures Appl. 78 (1999), 233-247.
  • [16] J. Rauch and B. A. Taylor, The Dirichlet problem for the multidimensional Monge-Ampère equation, Rocky Mountain J. Math. 7 (1977), 345-364.
  • [17] Y. Xing, Continuity of the complex Monge-Ampère operator, Proc. Amer. Math. Soc. 124 (1996), 457-467.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-apmv75z3p213bwm
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.