Holomorphic sectional curvature of some pseudoconvex domains
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- by Jeffery D. McNeal PDF
- Proc. Amer. Math. Soc. 107 (1989), 113-117 Request permission
Abstract:
The holomorphic sectional curvatures in the Bergman metric of a smooth bounded pseudoconvex domain in ${{\mathbf {C}}^2}$ are shown to be bounded in absolute value near a poinit of finite type in the boundaryReferences
- Stefan Bergman, The kernel function and conformal mapping, Second, revised edition, Mathematical Surveys, No. V, American Mathematical Society, Providence, R.I., 1970. MR 0507701 —, Sur la fonction-noyau d’un domaine..., Mem. Sci. Math. Paris 108 (1948).
- John S. Bland, The Einstein-Kähler metric on $\{|\textbf {z}|^2+|w|^{2p}<1\}$, Michigan Math. J. 33 (1986), no. 2, 209–220. MR 837579, DOI 10.1307/mmj/1029003350
- David W. Catlin, Estimates of invariant metrics on pseudoconvex domains of dimension two, Math. Z. 200 (1989), no. 3, 429–466. MR 978601, DOI 10.1007/BF01215657
- Robert E. Greene and Steven G. Krantz, Biholomorphic self-maps of domains, Complex analysis, II (College Park, Md., 1985–86) Lecture Notes in Math., vol. 1276, Springer, Berlin, 1987, pp. 136–207. MR 922321, DOI 10.1007/BFb0078959
- 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
- Shoshichi Kobayashi, Geometry of bounded domains, Trans. Amer. Math. Soc. 92 (1959), 267–290. MR 112162, DOI 10.1090/S0002-9947-1959-0112162-5
- Adam Korányi, A Schwarz lemma for bounded symmetric domains, Proc. Amer. Math. Soc. 17 (1966), 210–213. MR 199434, DOI 10.1090/S0002-9939-1966-0199434-2
- Jeffery D. McNeal, Boundary behavior of the Bergman kernel function in $\textbf {C}^2$, Duke Math. J. 58 (1989), no. 2, 499–512. MR 1016431, DOI 10.1215/S0012-7094-89-05822-5
- Ngaiming Mok and Shing-Tung Yau, Completeness of the Kähler-Einstein metric on bounded domains and the characterization of domains of holomorphy by curvature conditions, The mathematical heritage of Henri Poincaré, Part 1 (Bloomington, Ind., 1980) Proc. Sympos. Pure Math., vol. 39, Amer. Math. Soc., Providence, RI, 1983, pp. 41–59. MR 720056
- Shing Tung Yau, A general Schwarz lemma for Kähler manifolds, Amer. J. Math. 100 (1978), no. 1, 197–203. MR 486659, DOI 10.2307/2373880
Additional Information
- © Copyright 1989 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 107 (1989), 113-117
- MSC: Primary 32F30; Secondary 32H10, 53C55
- DOI: https://doi.org/10.1090/S0002-9939-1989-0979051-X
- MathSciNet review: 979051