# 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} }

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…

## 14 Citations

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