We prove that the sublevel set {z is an element of D : k(D)(z, z(0))-k(D)(f(z), w(0)) D if and only if mu <= 0. An analogous result is established also for the set {z is an element of D : 1-divided by f(z)divided by(2) < lambda(1 - divided by z divided by(2))}, lambda > 0. This extends a result of Solynin (2007) and solves a problem posed by Arango, Mejia and Pommerenke (2019). We also propose several open questions aiming at possible extensions to more general settings.
Hyperbolic convexity of holomorphic level sets
Gumenyuk, Pavel
2025-01-01
Abstract
We prove that the sublevel set {z is an element of D : k(D)(z, z(0))-k(D)(f(z), w(0)) D if and only if mu <= 0. An analogous result is established also for the set {z is an element of D : 1-divided by f(z)divided by(2) < lambda(1 - divided by z divided by(2))}, lambda > 0. This extends a result of Solynin (2007) and solves a problem posed by Arango, Mejia and Pommerenke (2019). We also propose several open questions aiming at possible extensions to more general settings.File in questo prodotto:
| File | Dimensione | Formato | |
|---|---|---|---|
|
2026.RMI.pdf
accesso aperto
Dimensione
453.16 kB
Formato
Adobe PDF
|
453.16 kB | Adobe PDF | Visualizza/Apri |
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
