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 -> a", (n) ) is reduced to investigating whether the complex manifold a(a) (ta parts per thousand yen0) f (t) (M) is biholomorphic to a domain in a", (n) . We apply such results to the study of univalent mappings f: B (n) -> a", (n) .

Arosio, L., Bracci, F., Hamada, H., Kohr, G. (2013). An abstract approach to Loewner chains. JOURNAL D'ANALYSE MATHEMATIQUE, 119(1), 89-114 [10.1007/s11854-013-0003-4].

An abstract approach to Loewner chains

AROSIO, LEANDRO;BRACCI, FILIPPO;
2013-01-01

Abstract

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 -> a", (n) ) is reduced to investigating whether the complex manifold a(a) (ta parts per thousand yen0) f (t) (M) is biholomorphic to a domain in a", (n) . We apply such results to the study of univalent mappings f: B (n) -> a", (n) .
2013
Pubblicato
Rilevanza internazionale
Articolo
Esperti anonimi
Settore MAT/03 - GEOMETRIA
English
Con Impact Factor ISI
Arosio, L., Bracci, F., Hamada, H., Kohr, G. (2013). An abstract approach to Loewner chains. JOURNAL D'ANALYSE MATHEMATIQUE, 119(1), 89-114 [10.1007/s11854-013-0003-4].
Arosio, L; Bracci, F; Hamada, H; Kohr, G
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2108/90252
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