Injectivity of mappings and solvability for partial differentiable operators
Global properties of systems of vector fields on compact Lie groups
| Full text | |
| Author(s): |
Braun, Francisco
;
dos Santos Filho, Jose Ruidival
;
Teixeira, Marco Antonio
Total Authors: 3
|
| Document type: | Journal article |
| Source: | ARCHIV DER MATHEMATIK; v. 119, n. 6, p. 17-pg., 2022-10-11. |
| Abstract | |
Let F : R-n -> R-n be a C-infinity map such that DF(x) is invertible for every x is an element of R-n. Although being a local diffeomorphism, F is not necessarily globally injective if n >= 2. Finding additional assumptions implying the global injectivity of F for n >= 2 is object of intense study in several areas of mathematics. In this paper, we revisit some assumptions and relations between them in the bi-dimensional case and discuss the natural higher dimensional situation. (AU) | |
| FAPESP's process: | 17/00136-0 - Global injectivity of maps in R^n |
| Grantee: | Francisco Braun |
| Support Opportunities: | Regular Research Grants |
| FAPESP's process: | 07/08231-0 - Geometric theory of PDE and several complex variables |
| Grantee: | Jorge Guillermo Hounie |
| Support Opportunities: | Research Projects - Thematic Grants |
| FAPESP's process: | 10/11323-7 - Injectivity of mappings and solvability for partial differentiable operators |
| Grantee: | Francisco Braun |
| Support Opportunities: | Scholarships in Brazil - Post-Doctoral |
| FAPESP's process: | 07/06896-5 - Geometry of control, dynamical and stochastic systems |
| Grantee: | Luiz Antonio Barrera San Martin |
| Support Opportunities: | Research Projects - Thematic Grants |
| FAPESP's process: | 14/26149-3 - Injectivity of polynomial maps in the plane |
| Grantee: | Francisco Braun |
| Support Opportunities: | Scholarships abroad - Research |