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Bulletin of the American Mathematical Society

The Bulletin publishes expository articles on contemporary mathematical research, written in a way that gives insight to mathematicians who may not be experts in the particular topic. The Bulletin also publishes reviews of selected books in mathematics and short articles in the Mathematical Perspectives section, both by invitation only.

ISSN 1088-9485 (online) ISSN 0273-0979 (print)

The 2020 MCQ for Bulletin of the American Mathematical Society is 0.84.

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Boundary behavior of the Carathéodory, Kobayashi, and Bergman metrics on strongly pseudoconvex domains in $\{\mathbf \{C\}\}^n$ with smooth boundary
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by Ian Graham PDF
Bull. Amer. Math. Soc. 79 (1973), 749-751
References
    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.
  • Klas Diederich, Das Randverhalten der Bergmanschen Kernfunktion und Metrik in streng pseudo-konvexen Gebieten, Math. Ann. 187 (1970), 9–36 (German). MR 262543, DOI 10.1007/BF01368157
  • Lars Hörmander, $L^{2}$ estimates and existence theorems for the $\bar \partial$ operator, Acta Math. 113 (1965), 89–152. MR 179443, DOI 10.1007/BF02391775
  • Shoshichi Kobayashi, Hyperbolic manifolds and holomorphic mappings, Pure and Applied Mathematics, vol. 2, Marcel Dekker, Inc., New York, 1970. MR 0277770
  • Hans-Jörg Reiffen, Die differentialgeometrischen Eigenschaften der invarianten Distanzfunktion von Carathéodory, Schr. Math. Inst. Univ. Münster 26 (1963), iii+66 (German). MR 158093
  • H. L. Royden, Remarks on the Kobayashi metric, Several complex variables, II (Proc. Internat. Conf., Univ. Maryland, College Park, Md., 1970) Lecture Notes in Math., Vol. 185, Springer, Berlin, 1971, pp. 125–137. MR 0304694
  • E. M. Stein, Boundary behavior of holomorphic functions of several complex variables, Mathematical Notes, No. 11, Princeton University Press, Princeton, N.J.; University of Tokyo Press, Tokyo, 1972. MR 0473215
  • 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
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Additional Information
  • 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