TY  - JOUR
AU  - Balreira, E. Cabral 
PY  - 2018
TI  - A Geometric Generalization of the Planar Gale-Nikaidô Theorem
JF  - Journal of Mathematics and Statistics
VL  - 14
IS  - 1
DO  - 10.3844/jmssp.2018.151.155
UR  - https://thescipub.com/abstract/jmssp.2018.151.155
AB  - 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.