4 papers
Global Gronwall Estimates for Integral Curves on Riemannian Manifolds
Michael Kunzinger, Hermann Schichl, Roland Steinbauer +1
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 s…
Generalized flows and singular ODEs on differentiable manifolds
Michael Kunzinger, Michael Oberguggenberger, Roland Steinbauer +1
Based on the concept of manifold valued generalized functions we initiate a study of nonlinear ordinary differential equations with singular (in particular: distributional) right h…
Intrinsic characterization of manifold-valued generalized functions
Michael Kunzinger, Roland Steinbauer, James A. Vickers
The concept of generalized functions taking values in a differentiable manifold is extended to a functorial theory. We establish several characterization results which allow a glob…
The thin string limit of Cosmic Strings coupled to gravity
K R P Sjodin, J A Vickers
The thin string limit of Cosmic Strings is investigated using a description in terms of Colombeau's theory of nonlinear generalised functions. It is shown that in this description…