We prove a necessary and sufficient condition for a local homeomorphism defined on an open, connected subset of a Euclidean space to be globally one-to-one and, at the same time, for the image to be convex. Among the applications we give a practical sufficient test of invertibility for twice differentiable local diffeomorphisms defined on a ball.
Local homeo- and diffeomorphisms: invertibility and convex image
ZAMPIERI, Gaetano;
1994-01-01
Abstract
We prove a necessary and sufficient condition for a local homeomorphism defined on an open, connected subset of a Euclidean space to be globally one-to-one and, at the same time, for the image to be convex. Among the applications we give a practical sufficient test of invertibility for twice differentiable local diffeomorphisms defined on a ball.
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