A logarithmic derivative lemma in several complex variables and its applications
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Abstract:
We give a logarithmic derivative lemma in several complex variables and its applications to meromorphic solutions of partial differential equations.References
- Carlos A. Berenstein and Roger Gay, Complex variables, Graduate Texts in Mathematics, vol. 125, Springer-Verlag, New York, 1991. An introduction. MR 1107514, DOI 10.1007/978-1-4612-3024-3
- Aldo Biancofiore and Wilhelm Stoll, Another proof of the lemma of the logarithmic derivative in several complex variables, Recent developments in several complex variables (Proc. Conf., Princeton Univ., Princeton, N. J., 1979) Ann. of Math. Stud., vol. 100, Princeton Univ. Press, Princeton, N.J., 1981, pp. 29–45. MR 627748
- Robert C. Gunning, Introduction to holomorphic functions of several variables. Vol. I, The Wadsworth & Brooks/Cole Mathematics Series, Wadsworth & Brooks/Cole Advanced Books & Software, Pacific Grove, CA, 1990. Function theory. MR 1052649
- W. K. Hayman, Meromorphic functions, Oxford Mathematical Monographs, Clarendon Press, Oxford, 1964. MR 0164038
- King-Lai Hiong, Sur les fonctions holomorphes dont les dérivées admettent une valeur exceptionnelle, Ann. Sci. Ecole Norm. Sup. (3) 72 (1955), 165–197 (French). MR 0074525
- Shoshichi Kobayashi, Hyperbolic complex spaces, Grundlehren der mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 318, Springer-Verlag, Berlin, 1998. MR 1635983, DOI 10.1007/978-3-662-03582-5
- Bao Qin Li, On entire solutions of Fermat type partial differential equations, Internat. J. Math. 15 (2004), no. 5, 473–485. MR 2072090, DOI 10.1142/S0129167X04002399
- Bao Qin Li, Entire solutions of certain partial differential equations and factorization of partial derivatives, Trans. Amer. Math. Soc. 357 (2005), no. 8, 3169–3177. MR 2135740, DOI 10.1090/S0002-9947-04-03745-6
- Joel L. Schiff, Normal families, Universitext, Springer-Verlag, New York, 1993. MR 1211641, DOI 10.1007/978-1-4612-0907-2
- Wilhelm Stoll, Holomorphic functions of finite order in several complex variables, Conference Board of the Mathematical Sciences Regional Conference Series in Mathematics, No. 21, American Mathematical Society, Providence, R.I., 1974. Expository Lectures from the CBMS Regional Conference held at the University of Wisconsin, Watewater, Wis., June 18–22, 1973. MR 0350052
- Wilhelm Stoll, Mehrfache Integrale auf komplexen Mannigfaltigkeiten, Math. Z. 57 (1952), 116–154 (German). MR 51941, DOI 10.1007/BF01192920
- Al Vitter, The lemma of the logarithmic derivative in several complex variables, Duke Math. J. 44 (1977), no. 1, 89–104. MR 432924
- Lo Yang, Value distribution theory, Springer-Verlag, Berlin; Science Press Beijing, Beijing, 1993. Translated and revised from the 1982 Chinese original. MR 1301781
- Zhuan Ye, On Nevanlinna’s second main theorem in projective space, Invent. Math. 122 (1995), no. 3, 475–507. MR 1359601, DOI 10.1007/BF01231453
Additional Information
- Bao Qin Li
- Affiliation: Department of Mathematics, Florida International University, Miami, Florida 33199
- MR Author ID: 249034
- Email: libaoqin@fiu.edu
- Received by editor(s): January 8, 2009
- Received by editor(s) in revised form: September 23, 2009
- Published electronically: June 27, 2011
- © Copyright 2011
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Trans. Amer. Math. Soc. 363 (2011), 6257-6267
- MSC (2010): Primary 32A22, 32A20, 30D35
- DOI: https://doi.org/10.1090/S0002-9947-2011-05226-8
- MathSciNet review: 2833553