Surjectivity of linear operators and semialgebraic global diffeomorphisms

We prove that a C ∞ semialgebraic local diffeomorphism of ℝ n with non-properness set having codimension greater than or equal to 2 is a global diffeomorphism if n − 1 suitable linear partial differential operators are surjective. Then we state a new analytic conjecture for a polynomial local diffeo...

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Bibliographic Details
Published in:Journal d'analyse mathématique (Jerusalem) 2023-09, Vol.150 (2), p.789-802
Main Authors: Braun, Francisco, Dias, Luis Renato Goncalves, Venato-Santos, Jean
Format: Article
Language:English
Subjects:
Abstract Harmonic Analysis
Analysis
Differential equations
Dynamical Systems and Ergodic Theory
Functional Analysis
Isomorphism
Linear operators
Mathematics
Mathematics and Statistics
Operators (mathematics)
Partial Differential Equations
Polynomials
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Summary:We prove that a C ∞ semialgebraic local diffeomorphism of ℝ n with non-properness set having codimension greater than or equal to 2 is a global diffeomorphism if n − 1 suitable linear partial differential operators are surjective. Then we state a new analytic conjecture for a polynomial local diffeomorphism of ℝ n . Our conjecture implies a very known conjecture of Z . Jelonek. We further relate the surjectivity of these operators with the fibration concept and state a general global injectivity theorem for semialgebraic mappings which turns out to unify and generalize previous results of the literature.
ISSN:0021-7670
1565-8538
DOI:10.1007/s11854-023-0286-z