Small volume on big $n$-spheres
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- by Christopher B. Croke PDF
- Proc. Amer. Math. Soc. 136 (2008), 715-717 Request permission
Abstract:
We consider Riemannian metrics on the $n$-sphere for $n\geq 3$ such that the distance between any pair of antipodal points is bounded below by 1. We show that the volume can be arbitrarily small. This is in contrast to the $2$-dimensional case where Berger has shown that $Area\geq 1/2$.References
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Additional Information
- Christopher B. Croke
- Affiliation: Department of Mathematics, University of Pennsylvania, Philadelphia, Pennsylvania 19104-6395
- MR Author ID: 204906
- Email: ccroke@math.upenn.edu
- Received by editor(s): November 9, 2006
- Published electronically: November 6, 2007
- Additional Notes: The author was supported by NSF grants DMS 02-02536 and 07-04145
- Communicated by: Jon G. Wolfson
- © Copyright 2007
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 136 (2008), 715-717
- MSC (2000): Primary 53C20
- DOI: https://doi.org/10.1090/S0002-9939-07-09079-X
- MathSciNet review: 2358513