On a Theorem of Bers, with Applications to the Study of Automorphism Groups of Domains
Canadian mathematical bulletin, Tome 59 (2016) no. 2, pp. 346-353

Voir la notice de l'article provenant de la source Cambridge University Press

We study and generalize a classical theoremof L. Bers that classifies domains up to biholomorphic equivalence in terms of the algebras of holomorphic functions on those domains. Then we develop applications of these results to the study of domains with noncompact automorphism group.
DOI : 10.4153/CMB-2015-078-8
Mots-clés : 32A38, 30H50, 32A10, 32M99, Bers’s theorem, algebras of holomorphic functions, noncompact automorphism group, biholomorphic equivalence
Krantz, Steven. On a Theorem of Bers, with Applications to the Study of Automorphism Groups of Domains. Canadian mathematical bulletin, Tome 59 (2016) no. 2, pp. 346-353. doi: 10.4153/CMB-2015-078-8
@article{10_4153_CMB_2015_078_8,
     author = {Krantz, Steven},
     title = {On a {Theorem} of {Bers,} with {Applications} to the {Study} of {Automorphism} {Groups} of {Domains}},
     journal = {Canadian mathematical bulletin},
     pages = {346--353},
     year = {2016},
     volume = {59},
     number = {2},
     doi = {10.4153/CMB-2015-078-8},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2015-078-8/}
}
TY  - JOUR
AU  - Krantz, Steven
TI  - On a Theorem of Bers, with Applications to the Study of Automorphism Groups of Domains
JO  - Canadian mathematical bulletin
PY  - 2016
SP  - 346
EP  - 353
VL  - 59
IS  - 2
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CMB-2015-078-8/
DO  - 10.4153/CMB-2015-078-8
ID  - 10_4153_CMB_2015_078_8
ER  - 
%0 Journal Article
%A Krantz, Steven
%T On a Theorem of Bers, with Applications to the Study of Automorphism Groups of Domains
%J Canadian mathematical bulletin
%D 2016
%P 346-353
%V 59
%N 2
%U http://geodesic.mathdoc.fr/articles/10.4153/CMB-2015-078-8/
%R 10.4153/CMB-2015-078-8
%F 10_4153_CMB_2015_078_8

[1] [1] Bers, L., On rings of analytic functions. Bull. Amer. Math. Soc. 54(1948), 311-315. Google Scholar | DOI

[2] [2] Fefferman, C., The Bergman kernel and biholomorphic mappings of pseudoconvex domains. Invent. Math. 26(1974), 1–65. Google Scholar | DOI

[3] [3] Graham, C. R., Scalar boundary invariants and the Bergman kernel. Complex analysis, II (College Park, Md., 1985-86), Lecture Notes in Math., 1276, Springer, Berlin, 1987, pp. 108–135. Google Scholar | DOI

[4] [4] Greene, R. E., Kim, K.-T., and Krantz, S. G., The geometry of complex domains.Progress in Mathematics, 291, BirkhâuserBoston, Boston, MA, 2011. Google Scholar | DOI

[5] [5] Greene, R. E. and Krantz, S. G., Deformations of complex structure, estimates for the d-equation, and stability of the Bergman kernel. Advances in Math. 43(1982), no. 1,1-86. Google Scholar | DOI | DOI

[6] [6] Kerzman, N. and Nagel, A., Finitely generated ideals in certain function algebras. J. Functional Analysis 7(1971), 212–215. Google Scholar | DOI

[7] [7] Klembeck, P. F., Kâhlermetrics of negative curvature, the Bergman metric near the boundary and the Kobayashi metric on smooth bounded strictly pseudoconvex sets. Indiana Univ. Math. J. 27(1978), no. 2, 275–282. Google Scholar | DOI

[8] [8] Krantz, S. G., Function theory of several complex variables. American Mathematical Society, Providence, RI, 2001. Google Scholar

[9] [9] Krantz, S. G., Geometric function theory. Explorations in complex analysis. Cornerstones, Birkhâuser Boston, Boston, MA, 2006. Google Scholar

[10] [10] Qi-Keng, L., On Kâhlermanifolds with constant curvature. Acta. Math.Sinica 16(1966), 269–281 (Chinese); Chinese Math. 9(1966), 283–298. Google Scholar

[11] [11] Ohsawa, T., A remark on the completeness of the Bergman metric. Proc. Japan Acad. Ser. A Math. Sci. 57(1981), no. 4, 238–240. Google Scholar | DOI

[12] [12] Siu, Y.-T., The d problem with uniform bounds on derivatives.Math. Ann. 207(1974), 163–176. Google Scholar | DOI

[13] [13] Wong, B., Characterizations of the ball in C” by its automorphism group. Invent. Math. 41(1977), no. 3, 253–257. Google Scholar | DOI

[14] [14] Zame, W. R., Homomorphisms of rings of germs of analytic functions. Proc. Amer. Math. Soc. 33(1972), 410–414. Google Scholar | DOI

[15] [15] Zame, W. R., Induced homomorphisms of algebras of analytic germs. Complex Analysis, 1972 (Proc. Conf, Rice Univ., Houston, Tex., 1972), Vol. II: Analysis on singularities. Rice Univ. Studies 59(1973), no. 2, 157–163. Google Scholar

Cité par Sources :