Abstract of a paper by Miek Messerschmidt and Marten Wortel
12 Nov
2015
12 Nov
'15
12:24 p.m.
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
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