Surjectivity of linear operators and semialgebraic global diffeomorphisms

• Published in: Journal 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
• Language: English
• 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

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...