We prove that for a strongly pseudoconvex domain D subset of Cn, the infinitesimal Caratheodory metric gC(z,v) and the infinitesimal Kobayashi metric gK(z,v) coincide if z is sufficiently close to bD and if v is sufficiently close to being tangential to bD. Also, we show that every two close points of D sufficiently close to the boundary and whose difference is almost tangential to bD can be joined by a (unique up to reparameterization) complex geodesic of D which is also a holomorphic retract of D. The same continues to hold if D is a worm domain, as long as the points are sufficiently close to a strongly pseudoconvex boundary point. We also show that a strongly pseudoconvex boundary point of a worm domain can be globally exposed; this has consequences for the behavior of the squeezing function.

Bracci, F., Fornaess, J.e., Wold, E.f. (2019). Comparison of invariant metrics and distances on strongly pseudoconvex domains and worm domains. MATHEMATISCHE ZEITSCHRIFT, 292(3-4), 879-893 [10.1007/s00209-018-2114-1].

Comparison of invariant metrics and distances on strongly pseudoconvex domains and worm domains

Bracci F.;
2019-01-01

Abstract

We prove that for a strongly pseudoconvex domain D subset of Cn, the infinitesimal Caratheodory metric gC(z,v) and the infinitesimal Kobayashi metric gK(z,v) coincide if z is sufficiently close to bD and if v is sufficiently close to being tangential to bD. Also, we show that every two close points of D sufficiently close to the boundary and whose difference is almost tangential to bD can be joined by a (unique up to reparameterization) complex geodesic of D which is also a holomorphic retract of D. The same continues to hold if D is a worm domain, as long as the points are sufficiently close to a strongly pseudoconvex boundary point. We also show that a strongly pseudoconvex boundary point of a worm domain can be globally exposed; this has consequences for the behavior of the squeezing function.
2019
Pubblicato
Rilevanza internazionale
Articolo
Esperti anonimi
Settore MAT/03 - GEOMETRIA
English
Bracci, F., Fornaess, J.e., Wold, E.f. (2019). Comparison of invariant metrics and distances on strongly pseudoconvex domains and worm domains. MATHEMATISCHE ZEITSCHRIFT, 292(3-4), 879-893 [10.1007/s00209-018-2114-1].
Bracci, F; Fornaess, Je; Wold, Ef
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2108/233044
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