Foundations of a nonlinear distributional geometry

DOI10.1023/A:1014554315909zbMath1012.46048arXivmath/0102019OpenAlexW3011526073MaRDI QIDQ1610249

Michael Kunzinger, Roland Steinbauer

Publication date: 19 August 2002

Published in: Acta Applicandae Mathematicae (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0102019

zbMATH Keywords

Colombeau algebrasalgebras of generalized functionsdistributional geometrygeneralized sections of vector bundles

Mathematics Subject Classification ID

Related Items (16)

Nonlinear generalized sections of vector bundles ⋮ Nonsmooth differential geometry and algebras of generalized functions ⋮ Sheaves of nonlinear generalized functions and manifold-valued distributions ⋮ On regularization of vector distributions on manifolds ⋮ Geodesics in nonexpanding impulsive gravitational waves with Λ. II ⋮ Point value characterizations and related results in the full Colombeau algebras \documentclass{article}\usepackage{amssymb}\begin{document}\pagestyle{empty}${{\mathcal {G}}^e(\Omega )}$\end{document} and \documentclass{article}\usepackage{amssymb}\begin{document}\pagestyle{empty}${{\mathcal {G}}^d(\Omega )}$\end{document} ⋮ An algebraic approach to manifold-valued generalized functions ⋮ Foundations of the calculus of variations in generalized function algebras ⋮ Distributional metrics and the action principle of Einstein–Hilbert gravity ⋮ Suppleness of the sheaf of algebras of generalized functions on manifolds ⋮ Generalized group actions in a global setting ⋮ Geometrical embeddings of distributions into algebras of generalized functions ⋮ The wave equation on singular space-times ⋮ Wave-type equations of low regularity ⋮ DIFFERENTIAL OPERATORS ON SCHWARTZ DISTRIBUTIONS ⋮ Generalized pseudo-Riemannian geometry

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