Fessler and Gutierrez [10, 13] proved that if a non-singular planar map has Jacobian matrix without eigenvalues in (0,+∞), then it is injective. We prove that the same holds replacing (0,+∞) with any unbounded curve disconnecting the upper (lower) complex half-plane. Additionally we prove that a Jacobian map (P,Q) is injective if ∂P/∂x + ∂Q/∂y is not a surjective function.
Injectivity of non-singular planar maps with disconnecting curves in the eigenvalues space / Sabatini, Marco. - In: TOPOLOGICAL METHODS IN NONLINEAR ANALYSIS. - ISSN 1230-3429. - STAMPA. - 62:1(2023), pp. 367-375. [10.12775/TMNA.2022.073]
Injectivity of non-singular planar maps with disconnecting curves in the eigenvalues space
Sabatini, Marco
2023-01-01
Abstract
Fessler and Gutierrez [10, 13] proved that if a non-singular planar map has Jacobian matrix without eigenvalues in (0,+∞), then it is injective. We prove that the same holds replacing (0,+∞) with any unbounded curve disconnecting the upper (lower) complex half-plane. Additionally we prove that a Jacobian map (P,Q) is injective if ∂P/∂x + ∂Q/∂y is not a surjective function.File in questo prodotto:
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