We prove a boundary version of the open mapping theorem for holomorphic maps between strongly pseudoconvex domains. That is, we prove that the local image of a holomorphic map $f:D\to D'$ close to a boundary regular contact point p\in \partial D where the Jacobian is bounded away from zero along normal non-tangential directions has to eventually contain every cone (and more generally every region which is Kobayashi asymptotic to a cone) with vertex at f(p).

Bracci, F., Fornaess, J. (2014). The range of holomorphic maps at boundary points. MATHEMATISCHE ANNALEN, 359(3-4), 909-927 [10.1007/s00208-014-1028-4].

### The range of holomorphic maps at boundary points

#### Abstract

We prove a boundary version of the open mapping theorem for holomorphic maps between strongly pseudoconvex domains. That is, we prove that the local image of a holomorphic map $f:D\to D'$ close to a boundary regular contact point p\in \partial D where the Jacobian is bounded away from zero along normal non-tangential directions has to eventually contain every cone (and more generally every region which is Kobayashi asymptotic to a cone) with vertex at f(p).
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Settore MAT/03 - Geometria
English
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Bracci, F., Fornaess, J. (2014). The range of holomorphic maps at boundary points. MATHEMATISCHE ANNALEN, 359(3-4), 909-927 [10.1007/s00208-014-1028-4].
Bracci, F; Fornaess, J
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2108/120235