We present several recent results dealing with the metric properties of domains in the complex Euclidean space . We provide with examples of domains, endowed with Finsler or Kähler metrics, that are (or are not) Gromov hyperbolic. We also present how different notions, such as the Gromov hyperbolicity, the holomorphic bisectional curvature or the d’Angelo type may be related for smooth bounded domains in . We also present several open questions in the core of the paper.
Mots clés : Complex manifolds, Finsler metric, Kähler metric, Gromov hyperbolicity, holomorphic bisectional curvature, d’Angelo finite type
@article{TSG_2017-2019__35__23_0, author = {Gaussier, Herv\'e}, title = {On the {Gromov} hyperbolicity of domains in $\protect \mathbb{C}^n$}, journal = {S\'eminaire de th\'eorie spectrale et g\'eom\'etrie}, pages = {23--42}, publisher = {Institut Fourier}, address = {Grenoble}, volume = {35}, year = {2017-2019}, doi = {10.5802/tsg.362}, language = {en}, url = {http://archive.numdam.org/articles/10.5802/tsg.362/} }
TY - JOUR AU - Gaussier, Hervé TI - On the Gromov hyperbolicity of domains in $\protect \mathbb{C}^n$ JO - Séminaire de théorie spectrale et géométrie PY - 2017-2019 SP - 23 EP - 42 VL - 35 PB - Institut Fourier PP - Grenoble UR - http://archive.numdam.org/articles/10.5802/tsg.362/ DO - 10.5802/tsg.362 LA - en ID - TSG_2017-2019__35__23_0 ER -
%0 Journal Article %A Gaussier, Hervé %T On the Gromov hyperbolicity of domains in $\protect \mathbb{C}^n$ %J Séminaire de théorie spectrale et géométrie %D 2017-2019 %P 23-42 %V 35 %I Institut Fourier %C Grenoble %U http://archive.numdam.org/articles/10.5802/tsg.362/ %R 10.5802/tsg.362 %G en %F TSG_2017-2019__35__23_0
Gaussier, Hervé. On the Gromov hyperbolicity of domains in $\protect \mathbb{C}^n$. Séminaire de théorie spectrale et géométrie, Tome 35 (2017-2019), pp. 23-42. doi : 10.5802/tsg.362. http://archive.numdam.org/articles/10.5802/tsg.362/
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