Remote Access Bulletin of the American Mathematical Society

Bulletin of the American Mathematical Society

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

 
 

 

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
Full-text PDF

References | Similar Articles | Additional Information

References [Enhancements On Off] (What's this?)

  • 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. 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, https://doi.org/10.1002/cpa.3160330404
  • 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. Robert E. Greene and Steven G. Krantz, The automorphism groups of strongly pseudoconvex domains, Math. Ann. 261 (1982), no. 4, 425–446. MR 682655, https://doi.org/10.1007/BF01457445
  • 8. M. Gromov, Manifolds of negative curvature, J. Differential Geom. 13 (1978), no. 2, 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 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, https://doi.org/10.2307/1971149
  • 13. 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, https://doi.org/10.2307/1971321
  • 14. B. Wong, Characterizations of the ball in C, Invent. Math. 41 (1977), 253-257. MR 492401

Similar Articles

Retrieve articles in Bulletin of the American Mathematical Society with MSC (1980): 32H10, 35N15, 32G05, 32H05, 53C55

Retrieve articles in all journals with MSC (1980): 32H10, 35N15, 32G05, 32H05, 53C55


Additional Information

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

American Mathematical Society