## View abstract

### 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. document.getElementById('cloakc3c989c553a94962f5afedffb3026f62').innerHTML = ''; var prefix = '&#109;a' + 'i&#108;' + '&#116;o'; var path = 'hr' + 'ef' + '='; var addyc3c989c553a94962f5afedffb3026f62 = '&#111;l&#105;v&#105;&#97;.g&#117;t&#117;' + '&#64;'; addyc3c989c553a94962f5afedffb3026f62 = addyc3c989c553a94962f5afedffb3026f62 + '&#117;n&#105;s&#111;n' + '&#46;' + 'mx'; var addy_textc3c989c553a94962f5afedffb3026f62 = '&#111;l&#105;v&#105;&#97;.g&#117;t&#117;' + '&#64;' + '&#117;n&#105;s&#111;n' + '&#46;' + 'mx';document.getElementById('cloakc3c989c553a94962f5afedffb3026f62').innerHTML += '<a ' + path + '\'' + prefix + ':' + addyc3c989c553a94962f5afedffb3026f62 + '\'>'+addy_textc3c989c553a94962f5afedffb3026f62+'<\/a>';

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.