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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
DOI: https://doi.org/10.1090/S0002-9904-1973-13297-5
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. K. Diederich, Das Randverhalten der Bergmanschen Kernfunktion und Metrik in streng pseudo-konvexen Gebieten, Math. Ann. 187 (1970), 9-36. MR 262543
  • 5. L. Hörmander, L2 estimates and existence theorems for the $\bar \partial $ operator, Acta. Math. 113 (1965), 89-152. MR 31 #3691. MR 179443
  • 6. S. Kobayshi, Hyperbolic manifolds and holomorphic mappings, Pure and Appl. Math., vol. 2, Marcel Dekker, 1970. MR 43 #3503. MR 277770
  • 7. H.-J. Reiffen, Die differentialgeometrischen Eigenschaften der invarianten Distanzfunktion von Carathéodory, Sch. Math. Inst. Univ. Münster, Heft 26, 1963. MR 28 # 1320. MR 158093
  • 8. H. L. Royden, Remarks on the Kobayashi metric. Several complex variables. II, Maryland 1970, 125-137; Springer-Verlag 1971. MR 304694
  • 9. E. M. Stein, Boundary behaviour of holomorphic functions of several complex variables, Princeton, Univ. Press, Princeton, N. J., 1972. MR 473215
  • 10. G. Henkin, Analytic polyhedra are not analytically equivalent to strictly pseudoconvex domains, Dokl. Akad. Nauk. SSSR (to appear). MR 328125

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DOI: https://doi.org/10.1090/S0002-9904-1973-13297-5

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