Skip to Main Content

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.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

The stability of the Bergman kernel and the geometry of the Bergman metric
HTML articles powered by AMS MathViewer

by Robert E. Greene and Steven G. Krantz PDF
Bull. Amer. Math. Soc. 4 (1981), 111-115
References
    1. L. Boutet de Monvel and J. Sjöstrand, Sur la singularité des noyaux de Bergman et de Szegö, Soc. Mat. de France Asterisque 34-35 (1976), 123-164.
  • Shiu Yuen Cheng and Shing Tung Yau, On the existence of a complete Kähler metric on noncompact complex manifolds and the regularity of Fefferman’s equation, Comm. Pure Appl. Math. 33 (1980), no. 4, 507–544. MR 575736, DOI 10.1002/cpa.3160330404
  • Charles Fefferman, The Bergman kernel and biholomorphic mappings of pseudoconvex domains, Invent. Math. 26 (1974), 1–65. MR 350069, DOI 10.1007/BF01406845
  • G. B. Folland and J. J. Kohn, The Neumann problem for the Cauchy-Riemann complex, Annals of Mathematics Studies, No. 75, Princeton University Press, Princeton, N.J.; University of Tokyo Press, Tokyo, 1972. MR 0461588
  • 5. R. E. Greene and S. G. Krantz, Stability of the Bergman kernel and curvature properties of bounded domains, Proc. Princeton Conf. on Several Complex Variables, 1979 (to appear). 6. R. E. Greene and S. G. Krantz, Deformation of complex structures, estimates for the (partial d) equation, and stability of the Bergman kernel, Advances in Math, (to appear).
  • Robert E. Greene and Steven G. Krantz, The automorphism groups of strongly pseudoconvex domains, Math. Ann. 261 (1982), no. 4, 425–446. MR 682655, DOI 10.1007/BF01457445
  • M. Gromov, Manifolds of negative curvature, J. Differential Geometry 13 (1978), no. 2, 223–230. MR 540941, DOI 10.4310/jdg/1214434487
  • Norberto Kerzman, The Bergman kernel function. Differentiability at the boundary, Math. Ann. 195 (1972), 149–158. MR 294694, DOI 10.1007/BF01419622
  • Paul F. Klembeck, Kähler metrics of negative curvature, the Bergmann metric near the boundary, and the Kobayashi metric on smooth bounded strictly pseudoconvex sets, Indiana Univ. Math. J. 27 (1978), no. 2, 275–282. MR 463506, DOI 10.1512/iumj.1978.27.27020
  • 11. Lu Qi-Keng (= K. H. Look), On Kähler manifolds with constant negative curvature, Acta Math. Sinica 16 (1966), 269-281 (Chinese) = Chinese Math. 9 (1966), 283-298.
  • G. D. Mostow and Yum Tong Siu, A compact Kähler surface of negative curvature not covered by the ball, Ann. of Math. (2) 112 (1980), no. 2, 321–360. MR 592294, DOI 10.2307/1971149
  • Yum Tong Siu, The complex-analyticity of harmonic maps and the strong rigidity of compact Kähler manifolds, Ann. of Math. (2) 112 (1980), no. 1, 73–111. MR 584075, DOI 10.2307/1971321
  • B. Wong, Characterization of the unit ball in $\textbf {C}^{n}$ by its automorphism group, Invent. Math. 41 (1977), no. 3, 253–257. MR 492401, DOI 10.1007/BF01403050
Similar Articles
Additional Information
  • Journal: Bull. Amer. Math. Soc. 4 (1981), 111-115
  • MSC (1980): Primary 32H10, 35N15; Secondary 32G05, 32H05, 53C55
  • DOI: https://doi.org/10.1090/S0273-0979-1981-14874-6
  • MathSciNet review: 590822