Pseudohermitian invariants and classification of CR mappings in generalized ellipsoids
Roberto Monti, Daniele Morbidelli
TL;DR
This paper classifies local CR diffeomorphisms of strictly pseudoconvex surfaces, especially generalized ellipsoids, using Tanaka-Webster invariants, Chern-Moser invariants, and their transformation properties.
Contribution
It introduces a classification method for CR mappings in generalized ellipsoids based on pseudohermitian invariants and their transformation formulas.
Findings
Complete classification of local CR mappings in generalized ellipsoids
Utilization of Tanaka-Webster and Chern-Moser invariants for classification
Advancement in understanding CR geometry of pseudoconvex surfaces
Abstract
We discuss the problem of classifying all local CR diffeomorphisms of a strictly pseudoconvex surface. Our method exploits the Tanaka--Webster pseudohermitian invariants, their transformation formulae, and the Chern--Moser invariants. Our main application concerns a class of generalized ellipsoids where we classify all local CR mappings.
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Taxonomy
TopicsHolomorphic and Operator Theory · Analytic and geometric function theory · Algebraic and Geometric Analysis