Skip to Main Content

Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

The intersection of an entire holomorphic mapping and a complex Monge-Ampère current with a bounded potential
HTML articles powered by AMS MathViewer

by Yusaku Tiba PDF
Proc. Amer. Math. Soc. 144 (2016), 5265-5273 Request permission

Abstract:

In this paper, we study the intersection of an entire holomorphic mapping and a complex Monge-Ampère current with a bounded potential. By using our results, we show a sufficient condition involving order functions of an entire holomorphic mapping such that the complement of its image is a pluripolar set.
References
  • Eric Bedford and B. A. Taylor, The Dirichlet problem for a complex Monge-Ampère equation, Invent. Math. 37 (1976), no. 1, 1–44. MR 445006, DOI 10.1007/BF01418826
  • Zbigniew Błocki, Estimates for the complex Monge-Ampère operator, Bull. Polish Acad. Sci. Math. 41 (1993), no. 2, 151–157 (1994). MR 1414762
  • Daniel Burns and Nessim Sibony, Limit currents and value distribution of holomorphic maps, Ann. Inst. Fourier (Grenoble) 62 (2012), no. 1, 145–176 (English, with English and French summaries). MR 2986269
  • James A. Carlson and Phillip A. Griffiths, The order functions for entire holomorphic mappings, Value distribution theory (Proc. Tulane Univ. Program, Tulane Univ., New Orleans, La., 1972-1973) Dekker, New York, 1974, pp. 225–248. MR 0404699
  • J. P. Demailly, Complex analytic and differential geometry, OpenContent Book. Version of Thursday June 21, 2012. Available at the author’s web page.
  • Jean-Pierre Demailly, Regularization of closed positive currents and intersection theory, J. Algebraic Geom. 1 (1992), no. 3, 361–409. MR 1158622
  • J. P. Demailly, Potential Theory in Several Complex Variables, complément à un exposé rédigé le cadre de la conférence de Trento en 1992, available at the author’s web page.
  • Vincent Guedj and Ahmed Zeriahi, Intrinsic capacities on compact Kähler manifolds, J. Geom. Anal. 15 (2005), no. 4, 607–639. MR 2203165, DOI 10.1007/BF02922247
  • Shoshichi Kobayashi and Takushiro Ochiai, Meromorphic mappings onto compact complex spaces of general type, Invent. Math. 31 (1975), no. 1, 7–16. MR 402127, DOI 10.1007/BF01389863
  • Robert E. Molzon, Sets omitted by equidimensional holomorphic mappings, Amer. J. Math. 101 (1979), no. 6, 1271–1283. MR 548881, DOI 10.2307/2374140
  • Junjiro Noguchi and Takushiro Ochiai, Geometric function theory in several complex variables, Translations of Mathematical Monographs, vol. 80, American Mathematical Society, Providence, RI, 1990. Translated from the Japanese by Noguchi. MR 1084378, DOI 10.1090/mmono/080
Similar Articles
  • Retrieve articles in Proceedings of the American Mathematical Society with MSC (2010): 32H30, 32U40
  • Retrieve articles in all journals with MSC (2010): 32H30, 32U40
Additional Information
  • Yusaku Tiba
  • Affiliation: Graduate School of Mathematical Sciences, University of Tokyo, 3-8-1 Komaba, Meguro-ku, Tokyo, Japan
  • Email: tiba@ms.u-tokyo.ac.jp
  • Received by editor(s): February 18, 2016
  • Published electronically: July 26, 2016
  • Communicated by: Franc Forstneric
  • © Copyright 2016 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 144 (2016), 5265-5273
  • MSC (2010): Primary 32H30, 32U40
  • DOI: https://doi.org/10.1090/proc/13295
  • MathSciNet review: 3556270