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Bulletin of the American Mathematical Society
Bulletin of the American Mathematical Society
ISSN 1088-9485(online) ISSN 0273-0979(print)

 

Boundary behavior of the Carathéodory, Kobayashi, and Bergman metrics on strongly pseudoconvex domains in ${\mathbf{C}}^n $ with smooth boundary


Author: Ian Graham
Journal: Bull. Amer. Math. Soc. 79 (1973), 749-751
MSC (1970): Primary 32D15, 32H15; Secondary 32E30, 32H10
MathSciNet review: 0324076
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  • 1. S. Bergman, Über die Kernfunktion und ihr Verhalten am Rande. I, II, J. Reine Angew. Math. 169 (1933), 1-42; 172 (1934), 89-128.
  • 2. C. Carathéodory, Über das Schwarze Lemma bei analytischen Funktionen von zwei komplexen Veränderlichen, Math. Ann. 97 (1926), 76-98.
  • 3. C. Carathéodory, Über die Geometrie der analytischen Abbildungen, die durch analytische Funktionen von zwei Veränderlichen vermittelt werden, Abh. Math. Sem. Univ. Hamburg. 6 (1928), 97-145.
  • 4. Klas Diederich, Das Randverhalten der Bergmanschen Kernfunktion und Metrik in streng pseudo-konvexen Gebieten, Math. Ann. 187 (1970), 9–36 (German). MR 0262543 (41 #7149)
  • 5. Lars Hörmander, 𝐿² estimates and existence theorems for the ∂\ operator, Acta Math. 113 (1965), 89–152. MR 0179443 (31 #3691)
  • 6. Shoshichi Kobayashi, Hyperbolic manifolds and holomorphic mappings, Pure and Applied Mathematics, vol. 2, Marcel Dekker, Inc., New York, 1970. MR 0277770 (43 #3503)
  • 7. Hans-Jörg Reiffen, Die differentialgeometrischen Eigenschaften der invarianten Distanzfunktion von Carathéodory, Schr. Math. Inst. Univ. Münster No. 26 (1963), iii+66 (German). MR 0158093 (28 #1320)
  • 8. H. L. Royden, Remarks on the Kobayashi metric, Several complex variables, II (Proc. Internat. Conf., Univ. Maryland, College Park, Md., 1970) Springer, Berlin, 1971, pp. 125–137. Lecture Notes in Math., Vol. 185. MR 0304694 (46 #3826)
  • 9. E. M. Stein, Boundary behavior of holomorphic functions of several complex variables, Princeton University Press, Princeton, N.J.; University of Tokyo Press, Tokyo, 1972. Mathematical Notes, No. 11. MR 0473215 (57 #12890)
  • 10. G. M. Henkin, An analytic polyhedron is not holomorphically equivalent to a strictly pseudoconvex domain, Dokl. Akad. Nauk SSSR 210 (1973), 1026–1029 (Russian). MR 0328125 (48 #6467)

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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9904-1973-13297-5
PII: S 0002-9904(1973)13297-5