Year: 2017
Type: article
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 in finite time or converges to a closed geodesic. The main result is that this conjecture is valid for nonpositively curved compact manifolds.
Source: Pacific Journal of Mathematics
Author: Dmitri Gekhtman
Institution: California Institute of Technology
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2254088698