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 inJournal d'analyse mathématique (Jerusalem) Vol. 150; no. 2; pp. 789 - 802
Main Authors Braun, Francisco, Dias, Luis Renato Goncalves, Venato-Santos, Jean
Format Journal Article
LanguageEnglish
Published Jerusalem The Hebrew University Magnes Press 01.09.2023
Springer Nature B.V
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