6533b86efe1ef96bd12ccb17
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Conformal equivalence of visual metrics in pseudoconvex domains
Luca CapognaEnrico Le DonneEnrico Le Donnesubject
Mathematics - Differential GeometryComputer Science::Machine LearningPure mathematicsGeneral Mathematics32T15 32Q45 32H40 53C23 53C17Rigidity (psychology)Conformal mapMathematical proofComputer Science::Digital Libraries01 natural sciencesdifferentiaaligeometriaStatistics::Machine LearningCorollaryMathematics - Metric Geometry0103 physical sciencesFOS: MathematicsMathematics::Metric GeometryComplex Variables (math.CV)0101 mathematicsEquivalence (formal languages)kompleksifunktiotMathematicsMathematics - Complex VariablesMathematics::Complex Variables010102 general mathematicsMetric Geometry (math.MG)16. Peace & justiceDifferential Geometry (math.DG)Bounded functionComputer Science::Mathematical Software010307 mathematical physicsdescription
We refine estimates introduced by Balogh and Bonk, to show that the boundary extensions of isometries between smooth strongly pseudoconvex domains in $\C^n$ are conformal with respect to the sub-Riemannian metric induced by the Levi form. As a corollary we obtain an alternative proof of a result of Fefferman on smooth extensions of biholomorphic mappings between pseudoconvex domains. The proofs are inspired by Mostow's proof of his rigidity theorem and are based on the asymptotic hyperbolic character of the Kobayashi or Bergman metrics and on the Bonk-Schramm hyperbolic fillings.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2017-03-01 | Mathematische Annalen |