Hostname: page-component-74656f9884-8r8nv Total loading time: 0 Render date: 2026-11-08T06:06:43.131Z Has data issue: false hasContentIssue false
  • English
  • Français

A Packing Problem for Holomorphic Curves

Published online by Cambridge University Press:  11 January 2016

Masaki Tsukamoto
Masaki Tsukamoto*
Affiliation:
Department of Mathematics, Faculty of Science, Kyoto University, Kyoto 606-8502, Japan, tukamoto@math.kyoto-u.ac.jp
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the 'Save PDF' action button.

We propose a new approach to the value distribution theory of entire holomorphic curves. We define packing density of Brody curves, and show that it has various non-trivial properties. The packing density of Brody curves can be considered as an infinite dimensional version of characteristic number, and it has an application to Gromov’s mean dimension theory.

Keywords

32H30

Information

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 194 , 2009 , pp. 33 - 68
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 2009

References

[1] Berteloot, F. and Duval, J., Sur l’hyperbolicité de certains complémentaires, Enseign. Math., 47 (2001), 253–267.Google Scholar
[2] Brody, R., Compact manifolds and hyperbolicity, Trans. Amer. Math. Soc., 235 (1978), 213–219.Google Scholar
[3] Calabi, E., Isometric imbedding of complex manifolds, Ann. of Math., 58 (1953), 1–23.Google Scholar
[4] Clunie, J. and Hayman, W. K., The spherical derivative of integral and meromorphic functions, Comment. Math. Helv., 40 (1966), 117–148.CrossRefGoogle Scholar
[5] Donaldson, S. K. and Kronheimer, P. B., The geometry of four-manifolds, Oxford University Press, New York, 1990.Google Scholar
[6] Eremenko, A., Normal holomorphic curves from parabolic regions to projective spaces, preprint, Purdue University (1998) (arXiv:0710.1281).Google Scholar
[7] Gromov, M., Topological invariants of dynamical systems and spaces of holomorphic maps: I, Math. Phys. Anal. Geom., 2 (1999), 323–415.Google Scholar
[8] Ji, S., Inequality for the distortion function of invertible sheaves on abelian varieties, Duke Math. J., 58 (1989), 657–667.Google Scholar
[9] Kempf, G. R., Metrics on invertible sheaves on abelian varieties, Topics in algebraic geometry (Guanajuato, 1989), Aportaciones Mat. Notas Investigación, 5, Soc. Mat. Mexicana, México, 1992, pp. 107–108.Google Scholar
[10] Lindenstrauss, E., Mean dimension, small entropy factors and an embedding theorem, Inst. Hautes Etudes Sci. Publ. Math., 89 (1999), 227–262.Google Scholar
[11] Lindenstrauss, E. and Weiss, B., Mean topological dimension, Israel J. Math., 115 (2000), 1–24.Google Scholar
[12] Minda, D., Yosida functions, Lectures on complex analysis (Chi-Tai Chuang, ed.), World Sci. Publishing, Singapore, 1988, pp. 197–213.Google Scholar
[13] Mumford, D., Tata lectures on Theta, I, Birkhäuser, Boston-Basel-Stuttgart, 1983.Google Scholar
[14] Nevanlinna, R., Zur Theorie der meromorphen Funktionen, Acta Math., 46 (1925), 1–99.Google Scholar
[15] Tian, G., On a set of polarized Kähler metrics on algebraic manifolds, J. Differential Geom., 32 (1990), 99–130.Google Scholar
[16] Tsukamoto, M., On holomorphic curves in algebraic torus, J. Math. Kyoto Univ., 47–4 (2007), 881–892.Google Scholar
[17] Tsukamoto, M., Moduli space of Brody curves, energy and mean dimension, Nagoya Math. J., 192 (2008), 27–58.Google Scholar
[18] Zelditch, S., Szegö kernels and a theorem of Tian, Int. Math. Res. Notices, 6 (1998), 317–331.Google Scholar