Abstract and Applied Analysis
Volume 2003 (2003), Issue 2, Pages 75-81
Local properties of maps of the ball
Department of Mathematics, Weizmann Institute of Science, Rehovot, Israel
Received 25 January 2002
Copyright © 2003 Yakar Kannai. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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