This is an announcement for the paper "The intrinsic metric on the unit sphere of a normed space" by Miek Messerschmidt and Marten Wortel.

Abstract: Let $S$ denote the unit sphere of a real normed space. We show that the intrinsic metric on $S$ is strongly equivalent to the induced metric on $S$. Specifically, for all $x,y\in S$, [ |x-y|\leq d(x,y)\leq\sqrt{2}\pi|x-y|, ] where $d$ denotes the intrinsic metric on $S$.

Archive classification: math.FA math.MG

Mathematics Subject Classification: Primary:46B10. Secondary: 51F99, 46B07

Submitted from: mmesserschmidt@gmail.com

The paper may be downloaded from the archive by web browser from URL

http://front.math.ucdavis.edu/1510.07442

or

http://arXiv.org/abs/1510.07442