Comptes Rendus
no. 6
Geometry/Complex analysis
Homotopic equivalence of rational proper holomorphic discs of bounded symmetric domains of type I
[Équivalence homotopique de disques rationnels propres holomorphiques de domaines bornés symétriques de type I]

Présenté par : the Editorial Board

Aeryeong Seo1
1 Department of Mathematics, Kyungpook National University, Daegu 41566, Republic of Korea
Comptes Rendus. Mathématique, Volume 357 (2019) no. 6, pp. 528-532.

Nous caractérisons les classes homotopiques de fonctions de Shilov rationnelles propres holomorphiques du disque unité à valeurs dans les domaines bornés symétriques à l'aide de disques de Shilov rationnels propres holomorphiques. Cette caractérisation généralise des résultats de D'Angelo–Huo–Xiao et de D'Angelo–Lebl, où les codomaines sont les boules unité.

We characterize homotopy classes of rational proper holomorphic Shilov maps from the unit disc to bounded symmetric domains of type I through rational proper holomorphic Shilov discs. This characterization generalizes results of D'Angelo–Huo–Xiao and D'Angelo–Lebl, where the codomains are the unit balls.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2019.06.005
Aeryeong Seo 1

1 Department of Mathematics, Kyungpook National University, Daegu 41566, Republic of Korea 
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     title = {Homotopic equivalence of rational proper holomorphic discs of bounded symmetric domains of type {I}},
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     pages = {528--532},
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Aeryeong Seo. Homotopic equivalence of rational proper holomorphic discs of bounded symmetric domains of type I. Comptes Rendus. Mathématique, Volume 357 (2019) no. 6, pp. 528-532. doi : 10.1016/j.crma.2019.06.005. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2019.06.005/

[1] W. Blaschke Eine Erweiterung des Satzes von Vitali über Folgen analytischer Funktionen, Ber. Verh. K. Sächs. Ges. Wiss. Leipz., Math.-Phys. Kl., Volume 67 (1915), pp. 194-200

[2] J.P. D'Angelo; Z. Huo; M. Xiao Proper holomorphic maps from the unit disk to some unit ball, Proc. Amer. Math. Soc., Volume 145 (2017) no. 6, pp. 2649-2660

[3] J.P. D'Angelo; J. Lebl Homotopy equivalence for proper holomorphic mappings, Adv. Math., Volume 286 (2016), pp. 160-180

[4] N. Mok Metric Rigidity Theorems on Hermitian Locally Symmetric Manifolds, Series in Pure Mathematics, vol. 6, World Scientific Publishing Co., Inc., Teaneck, NJ, USA, 1989 (xiv+278 pp. ISBN: 9971-50-800-1; 9971-50-802-8)

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