8 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…
Generalized pseudo-Riemannian geometry
Michael Kunzinger, Roland Steinbauer
Generalized tensor analysis in the sense of Colombeau's construction is employed to introduce a nonlinear distributional pseudo-Riemannian geometry. In particular, after deriving s…
Diffeomorphism invariant Colombeau Algebras. Part I: Local theory
Roland Steinbauer
This contribution is the first in a series of three: it reports on the construction of (a fine sheaf of) diffeomorphism invariant Colombeau algebras on open sets of Eucildean space…
Nonlinear distributional geometry and general relativity
Roland Steinbauer
This work reports on the construction of a nonlinear distributional geometry (in the sense of Colombeau's special setting) and its applications to general relativity with a special…