The ratio of invariant metrics on the annulus and theta functions

Kazuo Azukawa

Banach Center Publications (1995)

  • Volume: 31, Issue: 1, page 53-60
  • ISSN: 0137-6934

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Azukawa, Kazuo. "The ratio of invariant metrics on the annulus and theta functions." Banach Center Publications 31.1 (1995): 53-60. <http://eudml.org/doc/262574>.

@article{Azukawa1995,
author = {Azukawa, Kazuo},
journal = {Banach Center Publications},
keywords = {Carathéodory metric; Kobyashi metric; annulus; theta functions},
language = {eng},
number = {1},
pages = {53-60},
title = {The ratio of invariant metrics on the annulus and theta functions},
url = {http://eudml.org/doc/262574},
volume = {31},
year = {1995},
}

TY - JOUR
AU - Azukawa, Kazuo
TI - The ratio of invariant metrics on the annulus and theta functions
JO - Banach Center Publications
PY - 1995
VL - 31
IS - 1
SP - 53
EP - 60
LA - eng
KW - Carathéodory metric; Kobyashi metric; annulus; theta functions
UR - http://eudml.org/doc/262574
ER -

References

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  1. [1] K. Azukawa, Two intrinsic pseudo-metrics with pseudoconvex indicatrices and starlike circular domains J. Math. Soc. Japan 38 (1986), 627-647 Zbl0607.32015
  2. [2] K. Azukawa, The invariant pseudo-metric related to negative plurisubharmonic functions Kodai Math. J. 10 (1987), 83-92 Zbl0618.32020
  3. [3] E. Bedford and B. A. Taylor, Plurisubharmonic functions with logarithmic singularities Ann. Inst. Fourier (Grenoble) 38 (1988), 133-171 Zbl0626.32022
  4. [4] K. Chandrasekharan, Elliptic Functions Springer, New York, 1985. 
  5. [5] C. Carathéodory, Über die Geometrie der analytischen Abbildungen, die durch analytische Funktionen von zwei Veränderlichen vermittelt werden Abh. Math. Sem. Univ. Hamburg 6 (1928), 96-145 Zbl54.0372.04
  6. [6] S. Dineen, The Schwarz Lemma Clarendon Press, Oxford, 1989. 
  7. [7] J. E. Fornaess and B. Stensοness, Lectures on Counterexamples in Several Complex Variables Princeton Univ. Press, Princeton, 1987. 
  8. [8] M. Jarnicki and P. Pflug, Invariant pseudodistances and pseudometrics--Completeness and product property Ann. Polon. Math. 55 (1991), 169-189 Zbl0756.32016
  9. [9] M. Klimek, Extremal plurisubharmonic functions and invariant pseudodistances Bull. Soc. Math. France 113 (1985), 231-240 
  10. [10] M. Klimek, Infinitesimal pseudo-metrics and the Schwarz lemma Proc. Amer. Math. Soc. 105 (1989), 134-140 
  11. [11] M. Klimek, Pluripotential Theory Clarendon Press, Oxford, 1991. 
  12. [12] S. Kobayashi, Hyperbolic Manifolds and Holomorphic Mappings Marcel Dekker, New York, 1970. 
  13. [13] S. Kobayashi, Intrinsic distances, measures and geometric function theory Bull. Amer. Math. Soc. 82 (1976), 357-416 Zbl0346.32031
  14. [14] L. Lempert, La métrique de Kobayashi et la représentation des domaines sur la boule Bull. Soc. Math. France 109 (1981), 427-474 
  15. [15] E. A. Poletskiĭ and B. V. Shabat, Invariant metrics in: Encyclopedia of Mathematical Sciences 9, G. M. Khenkin (ed.), 1989, 63-111 
  16. [16] H. L. Royden, Remarks on the Kobayashi metric in: Lecture Notes in Math. 185, Springer, Berlin, 1971, 125-137 
  17. [17] R. R. Simha, The Carathéodory metric of the annulus Proc. Amer. Math. Soc. 50 (1975), 162-166 Zbl0281.30010

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