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The stability of the Bergman kernel and the geometry of the Bergman metric


Authors: Robert E. Greene and Steven G. Krantz
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
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  • 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.
  • 2. S.-Y Cheng and S. T. Yau, On the existence of complete Kähler metrics on noncompact manifolds and the regularity of Fefferman's equation, Comm. Pure Appl. Math. 23 (1980), 507-544. MR 575736
  • 3. C. Fefferman, The Bergman kernel and biholomorphic mappings of pseudoconvex domains, Invent. Math. 26 (1974), 1-65. MR 350069
  • 4. G. B. Folland and J. J. Kohn, The Neumann problem for the Cauchy-Riemann complex, Princeton Univ. Press, Princeton, N. J., 1972. MR 461588
  • 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).
  • 7. R. E. Greene and S. G. Krantz, The automorphism groups of strongly pseudoconvex domains (to appear). MR 682655
  • 8. M. Gromov, Manifolds of negative curvature, J. Differential Geometry 13 (1978), 223-230. MR 540941
  • 9. N. Kerzman, The Bergman kernel function. Differentiability at the boundary, Math. Ann. 195 (1972), 149-158. MR 294694
  • 10. P. Klembeck, Kähler metrics of negative curvature, the Bergman metric near the boundary and the Kobayashi metric on smoothly bounded strictly pseudoconvex sets, Indiana Univ. Math. J. 27 (1978), 275-282. MR 463506
  • 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.
  • 12. G. D. Mostow and Y. T. Siu, A compact Kähler surface of negative curvature not covered by the ball, Ann. of Math. 112 (1980), 321-360. MR 592294
  • 13. Y. T. Siu, The complex analyticity of harmonic maps and the strong rigidity of compact Kahler manifolds, Ann. of Math. 112 (1980), 73-112. MR 584075
  • 14. B. Wong, Characterizations of the ball in C, Invent. Math. 41 (1977), 253-257. MR 492401

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Additional Information

DOI: https://doi.org/10.1090/S0273-0979-1981-14874-6

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