Year: 2006
Type: preprint
Abstract: The main result given in Theorem~1.1 is a condition for a map $X$, defined on the complement of a disk $D$ in R^2 with values in R^2, to be extended to a topological embedding of R^2, not necessarily surjective. The map $X$ is supposed to be just differentiable with the condition that, for some $e>0,$ at each point the eigenvalues of the differential do not belong to the real interval $(-e,\infty).$ The extension is obtained by restricting X to the complement of some larger disc. The result has important connections with the property of asymptotic stability at infinity for differentiable vector fields.
Source: arXiv (Cornell University)
Authors: Gutierrez, Carlos, Rabanal, Roland
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4394668346