# Some remarks about metric spaces, spherical mappings, functions and their derivatives

@article{Semmes1996SomeRA,
title={Some remarks about metric spaces, spherical mappings, functions and their derivatives},
author={S. Semmes},
journal={Publicacions Matematiques},
year={1996},
volume={40},
pages={411-430}
}
• S. Semmes
• Published 1 July 1996
• Mathematics
• Publicacions Matematiques
If $p \in {\bold R}^n$, then we have the radial projection map from ${\bold R}^n \backslash \{p\}$ onto a sphere. Sometimes one can construct similar mappings on metric spaces even when the space is nontrivially different from Euclidean space, so that the existence of such a mapping becomes a sign of approximately Euclidean geometry. The existence of such spherical mappings can be used to derive estimates for the values of a function in terms of its gradient, which can then be used to derive…
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