Comparison of invariant functions and metrics

Kosiński, Łukasz

doi:10.1007/s00013-013-0596-y

Cited by 4 publications

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References 15 publications

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“…The theorem generalises a theorem of Kosinski [16], in which he shows that the invariant metrics coincide on some open set. Also, as pointed out by the referee, a version of the theorem for strongly pseudoconvex domains with boundaries of class C 6 , follows from the arguments in Section 4 in [4].…”

Section: Introductionmentioning

confidence: 61%

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

2018

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We prove that for a strongly pseudoconvex domain D ⊂ C n , the infinitesimal Carathéodory 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.

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Section: Introductionmentioning

confidence: 61%