naa a22 4500 510781543 CHVBK 20180411083249.0 cr unu---uuuuu 180411e20130401xx s 000 0 eng 10.1007/s11854-013-0003-4 doi (NATIONALLICENCE)springer-10.1007/s11854-013-0003-4 An abstract approach to Loewner chains [Elektronische Daten] [Leandro Arosio, Filippo Bracci, Hidetaka Hamada, Gabriela Kohr] We present a new geometric construction of Loewner chains in one and several complex variables which holds on complete hyperbolic complex manifolds and prove that there is essentially a one-to-one correspondence between evolution families of order d and Loewner chains of the same order. As a consequence, we obtain a univalent solution (f t : M → N) of any Loewner-Kufarev PDE. The problem of finding solutions given by univalent mappings (f t : M → ℂ n ) is reduced to investigating whether the complex manifold ∪ t≥0 f t (M) is biholomorphic to a domain in ℂ n . We apply such results to the study of univalent mappings f: B n → ℂ n . Hebrew University Magnes Press, 2013 Arosio Leandro Istituto Nazionale di Alta Matematica "Francesco Severi”, Città Universitaria, Piazzale Aldo Moro 5, 00185, Rome, Italy aut Bracci Filippo Dipartimento di Matematica, Università di Roma "Tor Vergata”, Via Della Ricerca Scientifica 1, 00133, Roma, Italy aut Hamada Hidetaka Faculty of Engineering, Kyushu Sangyo University, 3-1 Matsukadai 2-Chome, 813-8503, Higashi-ku Fukuoka, Japan aut Kohr Gabriela Faculty of Mathematics and Computer Science, Babeş-bolyai University, 1 M. Kogălniceanu Str., 400084, Cluj-Napoca, Romania aut Journal d'Analyse Mathématique The Hebrew University Magnes Press 119/1(2013-04-01), 89-114 0021-7670 119:1<89 2013 119 11854 https://doi.org/10.1007/s11854-013-0003-4 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s11854-013-0003-4 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Arosio Leandro Istituto Nazionale di Alta Matematica "Francesco Severi”, Città Universitaria, Piazzale Aldo Moro 5, 00185, Rome, Italy aut NATIONALLICENCE 700 1- Bracci Filippo Dipartimento di Matematica, Università di Roma "Tor Vergata”, Via Della Ricerca Scientifica 1, 00133, Roma, Italy aut NATIONALLICENCE 700 1- Hamada Hidetaka Faculty of Engineering, Kyushu Sangyo University, 3-1 Matsukadai 2-Chome, 813-8503, Higashi-ku Fukuoka, Japan aut NATIONALLICENCE 700 1- Kohr Gabriela Faculty of Mathematics and Computer Science, Babeş-bolyai University, 1 M. Kogălniceanu Str., 400084, Cluj-Napoca, Romania aut NATIONALLICENCE 773 0- Journal d'Analyse Mathématique The Hebrew University Magnes Press 119/1(2013-04-01), 89-114 0021-7670 119:1<89 2013 119 11854 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer