Abstract
In this chapter we present some classical results in several complex variables that relate boundary smoothness of domains with the geometric properties of holomorphic maps between these domains.
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References
Alexander, H.: Holomorphic map**s from the ball and polydisc. Math. Ann. 209, 249–256 (1974)
Lewy, H.: On the boundary behavior of holomorphic map**s. Acad. Naz. Lincei 35, 1–8 (1977)
Pinchuk, S.: Proper holomorphic maps of strictly pseudoconvex domains. Sibirsk. Math. J. 15, 909–917 (1974)
Pinchuk, S.: The analytic continuation of holomorphic map**s. Mat. Sb. 98(140), 416–435, 495–496 (1975)
Poncaré, H.: Les fonctions analytiques de deux variables et la représentation conforme. Rend. Circ. Mat. Palermo 23, 185–220 (1907)
Rosay, J.P.: Sur une caractérisation de la boule parmi les domains de \(\mathbb C^n\) par son groupe d’automorphisms. Ann. Inst. Fourier 29, 91–97 (1979)
Webster, S.: On the reflection principle in several complex variables. Proc. Am. Math. Soc. 71, 26–28 (1978)
Wong, B.: Characterization of the unit ball in \(\mathbb C^n\) by its automorphism group. Invent. Math. 41, 253–257 (1977)
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Pinchuk, S., Shafikov, R., Sukhov, A. (2023). Why Boundary Regularity?. In: Geometry of Holomorphic Map**s. Frontiers in Mathematics. Birkhäuser, Cham. https://doi.org/10.1007/978-3-031-37149-3_2
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DOI: https://doi.org/10.1007/978-3-031-37149-3_2
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Publisher Name: Birkhäuser, Cham
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