14 papers
Group invariants in algebras of generalized functions
Sanja Konjik, Michael Kunzinger
We study invariance properties of Colombeau generalized functions under actions of smooth Lie transformation groups. Several characterization results analogous to the smooth settin…
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…
Non-smooth differential geometry and algebras of generalized functions
Michael Kunzinger
Algebras of generalized functions offer possibilities beyond the purely distributional approach in modelling singular quantities in non-smooth differential geometry. This article p…
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 functions valued in a smooth manifold
Michael Kunzinger
Based on Colombeau's theory of algebras of generalized functions we introduce the concepts of generalized functions taking values in differentiable manifolds as well as of generali…