@article {10.3844/jmssp.2018.151.155,
article_type = {journal},
title = {A Geometric Generalization of the Planar Gale-Nikaidô Theorem},
author = {Balreira, E. Cabral},
volume = {14},
year = {2018},
month = {May},
pages = {151-155},
doi = {10.3844/jmssp.2018.151.155},
url = {https://thescipub.com/abstract/jmssp.2018.151.155},
abstract = {The Gale-Nikaidô Theorem establishes global injectivity of maps defined over rectangular regions provided the Jacobian matrix is a P-matrix. We provide a purely geometric generalization of this result in the plane by showing that if the image of each edge of the rectangular domain is realized as a graph of a function over the appropriate axis, then the map is injective. We also show that the hypothesis that the Jacobian matrix is a P-matrix is simply one way to analytically check this geometric condition.},
journal = {Journal of Mathematics and Statistics},
publisher = {Science Publications}
}