CaltechAUTHORS
  A Caltech Library Service

Cyclic pursuit on compact manifolds

Gekhtman, Dmitri (2017) Cyclic pursuit on compact manifolds. Pacific Journal of Mathematics, 289 (1). pp. 153-168. ISSN 0030-8730. https://resolver.caltech.edu/CaltechAUTHORS:20170712-131427876

[img] PDF - Published Version
See Usage Policy.

302Kb
[img] PDF - Submitted Version
See Usage Policy.

179Kb

Use this Persistent URL to link to this item: https://resolver.caltech.edu/CaltechAUTHORS:20170712-131427876

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.


Item Type:Article
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.2140/pjm.2017.289.153DOIArticle
http://msp.org/pjm/2017/289-1/p05.xhtmlPublisherArticle
https://arxiv.org/abs/1602.03259arXivDiscussion Paper
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.
Subject Keywords:cyclic pursuit, curve shortening, closed geodesics, nonpositive curvature
Issue or Number:1
Classification Code:MSC2010: primary 53B21; secondary 37D40
Record Number:CaltechAUTHORS:20170712-131427876
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20170712-131427876
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:79015
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:12 Jul 2017 21:25
Last Modified:03 Oct 2019 18:15

Repository Staff Only: item control page