Résumé
Nous étudions les courbes de Brody de l’espace projectif du point de vue de la théorie de Nevanlinna. Nous montrons en particulier que les courbes de Brody d’ordre \(>1\) dans \(P^1({\mathbf C})\) sont sans défaut.
References
Barrett, M., Eremenko, A.: A generalization of a theorem of Clunie and Hayman. Proc. Am. Math. Soc. 140, 1397–1402 (2012)
Clunie, J., Hayman, W.: The spherical derivative of integral and meromorphic functions. Commun. Math. Helv. 40, 117–148 (1966)
Eremenko, A.: Brody curves omitting hyperplanes. Ann. Acad. Sci. Fenn. Math. 35, 565–570 (2010)
Eremenko, A., Sodin, M.: The value distribution of meromorphic functions and meromorphic curves from the point of view of potential theory. St. Petersburg Math. J. 13, 109–136 (1992)
Grishin, A.: Sets of regular growth of entire functions. I (Russian). Teor. Funktsi Funktsional. Anal. i Prilozhen. 40, 36–47 (1983)
Hörmander, L.: The Analysis of Linear Partial Differential Operators I. Springer, Berlin (1990)
Kobayashi, S.: Hyperbolic Complex Spaces. Grund. Math. Wiss., vol. 318. Springer, Berlin (1998)
Mattila, P.: Geometry of Sets and Measures in Euclidean Spaces. Cambridge University Press, Cambridge (1995)
Nevanlinna, R.: Analytic Functions, Grund. Math. Wiss., vol. 162. Springer, Berlin (1970)
Øksendal, B.: Null sets for measures orthogonal to \(R(X)\). Am. J. Math. 94, 331–342 (1972)
Ransford, T.: Potential Theory in the Complex Plane. Cambridge University Press, Cambridge (1995)
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Da Costa, B.F.P., Duval, J. Sur les courbes de Brody dans \(P^n({\mathbf C})\) . Math. Ann. 355, 1593–1600 (2013). https://doi.org/10.1007/s00208-012-0831-z
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DOI: https://doi.org/10.1007/s00208-012-0831-z