Published July 2017
| Submitted + Published
Journal Article
Open
Cyclic pursuit on compact manifolds
- Creators
- Gekhtman, Dmitri
Abstract
We study a form of cyclic pursuit on Riemannian manifolds with positive injectivity radius. We conjecture that on a compact manifold, the piecewise geodesic loop formed by connecting consecutive pursuit agents either collapses to a point in finite time or converges to a closed geodesic. The main result is that this conjecture is valid for nonpositively curved compact manifolds.
Additional Information
© 2017 Mathematical Sciences Publishers. Received: 4 October 2016; Revised: 18 December 2016; Accepted: 29 December 2016; Published: 12 May 2017. This research was conducted mostly at the SUMMER@ICERM Undergraduate Summer Research Program in 2012. I would like to thank Tarik Aougab and Sergei Tabachnikov for their mentorship. I would like to thank Francisc Bozgan for pointing out the application of Jensen's inequality in Section 3. I would like to thank Anton Petrunin for a MathOverflow answer which helped with the proof of Proposition 8.1.Attached Files
Published - pjm-v289-n1-p05-s.pdf
Submitted - 1602.03259.pdf
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1602.03259.pdf
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Additional details
- Eprint ID
- 79015
- Resolver ID
- CaltechAUTHORS:20170712-131427876
- Created
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2017-07-12Created from EPrint's datestamp field
- Updated
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2021-11-15Created from EPrint's last_modified field