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Conformal equivalence of visual metrics in pseudoconvex domains
- Source :
- Mathematische Annalen
- Publication Year :
- 2020
-
Abstract
- 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.<br />20 pages
- Subjects :
- Mathematics - Differential Geometry
Computer Science::Machine Learning
Pure mathematics
General Mathematics
32T15, 32Q45, 32H40, 53C23, 53C17
Rigidity (psychology)
Conformal map
Mathematical proof
Computer Science::Digital Libraries
01 natural sciences
differentiaaligeometria
Statistics::Machine Learning
Corollary
Mathematics - Metric Geometry
0103 physical sciences
FOS: Mathematics
Mathematics::Metric Geometry
Complex Variables (math.CV)
0101 mathematics
Equivalence (formal languages)
kompleksifunktiot
Mathematics
Mathematics - Complex Variables
Mathematics::Complex Variables
010102 general mathematics
Metric Geometry (math.MG)
16. Peace & justice
Differential Geometry (math.DG)
Bounded function
Computer Science::Mathematical Software
010307 mathematical physics
Subjects
Details
- ISSN :
- 00255831
- Database :
- OpenAIRE
- Journal :
- Mathematische Annalen
- Accession number :
- edsair.doi.dedup.....f005493d3b768d69e9a41bf96f2c45b6
- Full Text :
- https://doi.org/10.1007/s00208-020-01962-1