Full paper in PDF:
$%M. Kunzinger, H. Schichl, R. Steinbauer, and J. A. Vickers, Global Gronwall estimates for integral curves on Riemannian manifolds, Rev. Mat. Complut. 19 (2006), no. 1, 133137. %$

Global Gronwall Estimates for Integral Curves on Riemannian Manifolds
Michael KUNZINGER, Hermann SCHICHL,
Roland STEINBAUER, and James A. VICKERS
Fakultät für Mathematik
Universität Wien
Nordbergstrasse 15
1090 Wien Austria

School of Mathematics
University of Southampton
Highfield, Southampton SO 17 1BJ UK
Received: June 13, 2005
Accepted: July 26, 2005
ABSTRACT

We prove Gronwall-type estimates for the distance of integral curves of smooth vector fields on a Riemannian manifold. Such estimates are of central importance for all methods of solving ODEs in a verified way, i.e., with full control of roundoff errors. Our results may therefore be seen as a prerequisite for the generalization of such methods to the setting of Riemannian manifolds.

Key words: Riemannian geometry, ordinary differential equations, Gronwall estimate.
2000 Mathematics Subject Classification:
53B21, 53C22, 34A26.