6 papers · 1 filter
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…
Foundations of a nonlinear distributional geometry
Michael Kunzinger, Roland Steinbauer
Co lombeau's construction of generalized functions (in its special variant) is extended to a theory of generalized sections of vector bundles. As particular cases, generalized tens…
On the foundations of nonlinear generalized functions I
Eva Farkas, Michael Grosser, Michael Kunzinger +1
We construct a diffeomorphism invariant (Colombeau-type) differential algebra canonically containing the space of distributions in the sense of L. Schwartz. Employing differential…