Geodesic
Generalization of Schwarz-Pick Lemma to Invariant Volume
Canadian journal of mathematics, Tome 21 (1969) no. 1, pp. 669-674

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

In this paper we give an extension of (6, Theorem 1), using a similar method of proof, to every homogeneous Siegel domain of second kind which can be mapped biholomorphically into a Kâhler manifold of a certain class (Theorem 1). Then by a well-known result of Vinberg, Gindikin, and Pjateckiï-Sapiro (10) that every bounded homogeneous domain D,contained in a complex euclidean space CN,can be mapped biholomorphically onto an affinely homogeneous Siegel domain of second kind, the theorem follows for D(Theorem 2). (6, Theorem 1) is a generalization of the Ahlfors version of the Schwarz-Pick lemma in C1 (1) to invariant volume for a star-like homogeneous bounded domain in CN;see also (4). In § 3 we give the inequality for a special non-symmetric Siegel domain of second kind using an explicit form of TD(z, )due to Lu (7). 
Hahn, K. T.; Mitchell, Josephine. Generalization of Schwarz-Pick Lemma to Invariant Volume. Canadian journal of mathematics, Tome 21 (1969) no. 1, pp. 669-674. doi: 10.4153/CJM-1969-076-2
@article{10_4153_CJM_1969_076_2,
     author = {Hahn, K. T. and Mitchell, Josephine},
     title = {Generalization of {Schwarz-Pick} {Lemma} to {Invariant} {Volume}},
     journal = {Canadian journal of mathematics},
     pages = {669--674},
     year = {1969},
     volume = {21},
     number = {1},
     doi = {10.4153/CJM-1969-076-2},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-1969-076-2/}
}
TY  - JOUR
AU  - Hahn, K. T.
AU  - Mitchell, Josephine
TI  - Generalization of Schwarz-Pick Lemma to Invariant Volume
JO  - Canadian journal of mathematics
PY  - 1969
SP  - 669
EP  - 674
VL  - 21
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CJM-1969-076-2/
DO  - 10.4153/CJM-1969-076-2
ID  - 10_4153_CJM_1969_076_2
ER  - 
%0 Journal Article
%A Hahn, K. T.
%A Mitchell, Josephine
%T Generalization of Schwarz-Pick Lemma to Invariant Volume
%J Canadian journal of mathematics
%D 1969
%P 669-674
%V 21
%N 1
%U http://geodesic.mathdoc.fr/articles/10.4153/CJM-1969-076-2/
%R 10.4153/CJM-1969-076-2
%F 10_4153_CJM_1969_076_2

[1] 1. Ahlfors, L. V., An extension of Schwarz's lemma, Trans. Amer. Math. Soc. 43 (1938), 359–364. Google Scholar

[2] 2. Behnke, H. and Thullen, P., Théorie der Funktionen mehrer komplexer Verdnderlichen, Ergebnisse der Math, und ihrer Grenzgebiete, Band 3 (Springer, Berlin, 1934). Google Scholar

[3] 3. Bergman, S., Sur les fonctions orthogonales de plusieurs variables complexes avec les applications à la théorie des fonctions analytiques, Mém. Sci. Math. no. 106 (Gauthier-Villars, Paris, 1947). Google Scholar

[4] 4. Bergman, S., Zur Théorie von pseudokonformen Abbildungen, Recueil Math. (N.S.) Nouv. sér. 1 (43) (1936), 79–96. Google Scholar

[5] 5. Fuks, B. A., Special chapters in the theory of analytic functions of several complex variables. Transi. Math. Monog., Vol. 14 (Amer. Math. Soc, Providence, R. I., 1965; Gosudarstv. Izdat. Fiz.-Mat. Lit., Moscow, 1963). Google Scholar

[6] 6. Hahn, K. T. and Mitchell, Josephine, Generalization of Schwarz-Pick lemma to invariant volume in a Kàhler manifold, Trans. Amer. Math. Soc. 128 (1967), 221–231. Google Scholar

[7] 7. Lu, R. Q., Harmonic functions in a class of non-symmetric transitive domains, Acta. Math. Sinica 15 (1965), No. 5, 614–650. Google Scholar

[8] 8. Pjateckiï-Sapiro, I. I., Geometry of classical domains and theory of automorphic functions (Fizmatgiz, Moscow, 1961). Google Scholar

[9] 9. Schaefer, H. H., Topological vector spaces (Macmillan, New York, 1966). Google Scholar

[10] 10. Vinberg, E. B., Gindikin, S. G., and Pjateckiï-Sapiro, I. I., Classification and canonical realization of complex homogeneous domains, Trudy Moscow Mat. Obsc. 12 (1963), 359-388 = Transi. Moscow Math. Soc. 12 (1963), 404–437. Google Scholar

Cité par Sources :