JOURNAL BROWSE
Search
Advanced SearchSearch Tips
HIGHER ORDER ASYMPTOTIC BEHAVIOR OF CERTAIN KÄHLER METRICS AND UNIFORMIZATION FOR STRONGLY PSEUDOCONVEX DOMAINS
facebook(new window)  Pirnt(new window) E-mail(new window) Excel Download
 Title & Authors
HIGHER ORDER ASYMPTOTIC BEHAVIOR OF CERTAIN KÄHLER METRICS AND UNIFORMIZATION FOR STRONGLY PSEUDOCONVEX DOMAINS
Joo, Jae-Cheon; Seo, Aeryeong;
  PDF(new window)
 Abstract
We provide some relations between CR invariants of boundaries of strongly pseudoconvex domains and higher order asymptotic behavior of certain complete Khler metrics of given domains. As a consequence, we prove a rigidity theorem of strongly pseudoconvex domains by asymptotic curvature behavior of metrics.
 Keywords
Bergman metric;Graham-Lee connection;CR invariants;
 Language
English
 Cited by
 References
1.
E. Barletta, On the boundary behavior of the holomorphic sectional curvature of the Bergman metric, Matematiche (Catania) 61 (2006), no. 2, 301-316.

2.
S. S. Chern and S. Ji, On the Riemann mapping theorem, Ann. of Math (2) 144 (1996), no. 2, 421-439. crossref(new window)

3.
S. S. Chern and J. K. Moser, Real hypersurfaces in complex manifolds, Acta Math. 133 (1974), 219-271. crossref(new window)

4.
C. Fefferman, On the Bergman kernel and biholomorphic mappings of pseudoconvex domains, Bull. Amer. Math. Soc. 80 (1974), no. 4, 667-669. crossref(new window)

5.
C. R. Graham and J. M. Lee, Smooth solutions of degenerate Laplacians on strictly pseudoconvex domains, Duke Math. J. 57 (1988), no. 3, 697-720. crossref(new window)

6.
K. Hirachi, Scalar pseudo-Hermitian invariants and the Szego kernel on three-dimensional CR manifolds, Complex geometry (Osaka, 1990), 67-76, Lecture Notes in Pure and Appl. Math., 143, Dekker, New York, 1993.

7.
K. T. Kim and J. Yu, Boundary behavior of the Bergman curvature in strictly pseudoconvex polyhedral domains, Pacific J. Math. 176 (1996), no. 1, 141-163.

8.
P. F. Klembeck, Kahler 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. crossref(new window)

9.
Q. K. Lu, On Kaehler manifolds with constant curvature, Acta Math. Sinica 16 (1966), 269-281 (Chinese); English transl. in Chinese Math. Acta 8 (1966), 283-298.

10.
N. Mok, The uniformization theorem for compact Kahler manifolds of nonnegative holomorphic bisectional curvature, J. Differential Geom. 27 (1988), no. 2, 179-214.

11.
S. Y. Nemirovskii and R. G. Shafikov, Uniformization of strictly pseudoconvex domains. I, Izv. Mat. 69 (2005), no. 6, 1189-1202. crossref(new window)

12.
S. Y. Nemirovskii and R. G. Shafikov, Uniformization of strictly pseudoconvex domains. II, Izv. Mat. 69 (2005), no. 6, 1203-1210. crossref(new window)

13.
S. I. Pincuk, Proper holomorphic maps of strictly pseudoconvex domains, (Russian) Sibirsk. Mat. Z. 15 (1974), 909-917, 959.

14.
N. Seshadri, Volume renormalization for complete Einstein-Kahler metrics, Differential Geom. Appl. 25 (2007), no. 4, 356-379. crossref(new window)

15.
Y.-T. Siu, The complex-analyticity of harmonic maps and the strong rigidity of compact Kahler manifolds, Ann. of Math. (2) 112 (1980), no. 1, 73-111. crossref(new window)

16.
Y.-T. Siu and S.-T. Yau, Complete Kahler manifolds with nonpositive curvature of faster than quadratic decay, Ann. of Math. (2) 105 (1977), no. 2, 225-264. crossref(new window)

17.
Y.-T. Siu and S.-T. Yau, Compact Kahler manifolds of positive bisectional curvature, Invent. Math. 59 (1980), no. 2, 189-204. crossref(new window)

18.
S. M. Webster, Pseudo-Hermitian structures on a real hypersurface, J. Differential Geom. 13 (1978), 25-41.