On the Hausdorff measures associated to the Carathéodory and Kobayashi metrics

J. Bland; Ian Graham

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze (1985)

  • Volume: 12, Issue: 4, page 503-514
  • ISSN: 0391-173X

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Bland, J., and Graham, Ian. "On the Hausdorff measures associated to the Carathéodory and Kobayashi metrics." Annali della Scuola Normale Superiore di Pisa - Classe di Scienze 12.4 (1985): 503-514. <http://eudml.org/doc/83965>.

@article{Bland1985,
author = {Bland, J., Graham, Ian},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
keywords = {Carathéodory metric; hyperbolic manifold; Poincaré metric; Kobayashi metrics; biholomorphic equivalence; Hausdorff measures; Finsler metrics},
language = {eng},
number = {4},
pages = {503-514},
publisher = {Scuola normale superiore},
title = {On the Hausdorff measures associated to the Carathéodory and Kobayashi metrics},
url = {http://eudml.org/doc/83965},
volume = {12},
year = {1985},
}

TY - JOUR
AU - Bland, J.
AU - Graham, Ian
TI - On the Hausdorff measures associated to the Carathéodory and Kobayashi metrics
JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
PY - 1985
PB - Scuola normale superiore
VL - 12
IS - 4
SP - 503
EP - 514
LA - eng
KW - Carathéodory metric; hyperbolic manifold; Poincaré metric; Kobayashi metrics; biholomorphic equivalence; Hausdorff measures; Finsler metrics
UR - http://eudml.org/doc/83965
ER -

References

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  1. [1] T.J. Barth, Some counterexamples concerning intrinsic distances, Proc. Amer. Math. Soc., 66 (1977), pp. 49-53. Zbl0331.32019MR454078
  2. [2] T.J. Barth, Convex domains and Kobayashi hyperbolicity, Proc. Amer. Math. Soc., 79 (1980), pp. 556-558. Zbl0438.32013MR572300
  3. [3] H. Busemann, Intrinsic area, Ann. of Math., 48 (1947), pp. 234-267. Zbl0029.35301MR20626
  4. [4] H. Busemann - W. Mayer, On the foundations of the calculus of variations, Trans. Amer. Math. Soc., 49 (1941), pp. 173-198. Zbl0024.41703MR3475JFM67.1036.03
  5. [5] D.A. Eisenman (= D.A. Pelles), Intrinsic measures on complex manifolds and holomorphic mappings, Mem. Amer. Math. Soc., no. 96, Amer. Math. Soc., Providence, 1970. Zbl0197.05901MR259165
  6. [6] H. Federer, Geometric Measure Theory, Springer-Verlag, New York, 1969. Zbl0176.00801MR257325
  7. [7] I. Graham - H. Wu, Some remarks on the intrinsic measures of Eisenman, Trans. Amer. Math. Soc.288 (1985), pp. 625-660. Zbl0582.32034MR776396
  8. [8] I. Graham - H. Wu, Characterizations of the unit ball B n in complex Euclidean space, Math. Z.189 (1985), pp. 449-456. Zbl0547.32013MR786275
  9. [9] S. Kobayashi, Hyperbolic Manifolds and Holomorphic Mappings, Marcel Dekker, New York, 1970. Zbl0207.37902MR277770
  10. [10] S. Kobayashi, Intrinsic distances, measures and geometric function theory, Bull. Amer. Math. Soc., 82 (1976), pp. 357-416. Zbl0346.32031MR414940
  11. [11] S.G. Krantz, Function Theory of Several Complex Variables, John Wiley & Sons, New York, 1982. Zbl0471.32008MR635928
  12. [12] L. Lempert, La métrique de Kobayashi et la representation des domaines sur la boule, Bull. Soc. Math. France, 109 (1981), pp. 427-474. Zbl0492.32025MR660145
  13. [13] L. Lempert, Holomorphic retracts and intrinsic metrics in convex domains, Anal. Math., 8 (1982), pp. 257-261. Zbl0509.32015MR690838
  14. [14] D.A. Pelles (= D.A. Eisenman), Holomorphic maps which preserve intrinsic measure, Amer. J. Math., 97 (1975), pp. 1-15. Zbl0303.32021MR367300
  15. [15] H.J. Reiffen, Die differentialgeometrischen Eigenschaften der invarianten Distanzfunktion von Caratheodory, Schriftenreihe Math. Inst. Univ. Münster, no. 26 (1963). Zbl0115.16303MR158093
  16. [16] H.L. Royden, Remarks on the Kobayashi metric, Several Complex Variables II (Proc. Intern. Conf. Univ. of Maryland, 1970), Lecture Notes in Mathematics, Vol. 185, Springer-Verlag, New York - Heidelberg - Berlin, 1971, pp. 125-137. Zbl0218.32012MR304694
  17. [17] H.L. Royden - P.-M. Wong, Caratheodory and Kobayashi metric on convex domains, to appear. 

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