Conformal equivalence of visual metrics in pseudoconvex domains
Capogna, L., & Le Donne, E. (2020). Conformal equivalence of visual metrics in pseudoconvex domains. Mathematische Annalen, 377(3-4), 1643-1672. https://doi.org/10.1007/s00208-020-01968-9
Published inMathematische Annalen
DisciplineGeometrinen analyysi ja matemaattinen fysiikkaMatematiikkaAnalyysin ja dynamiikan tutkimuksen huippuyksikköGeometric Analysis and Mathematical PhysicsMathematicsAnalysis and Dynamics Research (Centre of Excellence)
© Authors, 2020
We refine estimates introduced by Balogh and Bonk, to show that the boundary extensions of isometries between bounded, smooth strongly pseudoconvex domains in Cn 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 bounded smooth 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.
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Additional information about fundingOpen access funding provided by University of Jyväskylä (JYU).
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