Yakar Kannai, "Local properties of maps of the ball", Abstract and Applied Analysis, vol. 2003, Article ID 107103, 7 pages, 2003. https://doi.org/10.1155/S1085337503204012
Local properties of maps of the ball
Let be an essential map of into itself (i.e., is not homotopic to a constant mapping) admitting an extension mapping the closed unit ball into . Then, for every interior point of , there exists a point in such that the image of no neighborhood of is contained in a coordinate half space with on its boundary. Under additional conditions, the image of a neighborhood of covers a neighborhood of . Differential versions are valid for quasianalytic functions. These results are motivated by game-theoretic considerations.
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