Michael Kunzinger, Hermann Schichl, Roland Steinbauer, James A. Vickers
Published 2004-12-02, updated 2006-01-31Version 3
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.
Comments: 4 pages, 1 figure, correction of some misprints
Journal: Rev. Mat. Complut. 19 (2006), no. 1, 133--137.
Almost conformal transformation in a class of Riemannian manifolds
Examples of hypersurfaces flowing by curvature in a Riemannian manifold
A new connection in a Riemannian manifold
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