Session S14 - Global Injectivity, Jacobian Conjecture, and Related Topics

Monday, July 12, 14:50 ~ 15:40 UTC-3

Global inversion for metrically regular mapping between Banach spaces

Olivia Gutú

Universidad de Sonora, Mexico   -   This email address is being protected from spambots. You need JavaScript enabled to view it.

At the beginning of the last century, Hadamard introduced a global inversion criteria to ensure the existence and uniqueness of the nonlinear system given by a continuously differentiable local homeomorphism. From this beginning, seminal ideas have been developed over and over so far in different contexts but with four fundamental coincidence points: properness type conditions,path-lifting type conditions, metric-regularity asymptotic type conditions, Palais-Smale type conditions. In this talk we will present a recapitulation of global inverse theorems in the framework of metrically regular maps between Banach spaces. Metric regularity of a mapping at a point is a local concept involving certain rates and modulus, based on the Implicit Function Theorem, Banach Open Mapping Theorem and the Lyusternik-Graves Theorem. We consider this theoretical framework the ``definitive'' one since it encompasses the most relevant theorems in global inversion that have been documented in the literature in different contexts since Hadamard's original article of 1906: e.g. Gâteaux derivatives, generalized Jacobians, coderivatives, strict prederivatives, pseudo-Jacobians.

View abstract PDF