4.5 Article

Nonlinear generalized functions on manifolds

Publisher

ROYAL SOC
DOI: 10.1098/rspa.2020.0640

Keywords

nonlinear generalized functions; Colombeau algebra; diffeomorphism invariant

Funding

  1. Austrian Science Fund (FWF) [P26859, P30233]
  2. STFC grant [ST/R00045X]

Ask authors/readers for more resources

In this work, we adopt a new approach to the construction of a global theory of algebras of generalized functions on manifolds based on the concept of smoothing operators. This produces a generalization of previous theories in a form which is suitable for applications to differential geometry. The generalized Lie derivative is introduced and shown to extend the Lie derivative of Schwartz distributions. A new feature of this theory is the ability to define a covariant derivative of generalized scalar fields which extends the covariant derivative of distributions at the level of association. We end by sketching some applications of the theory. This work also lays the foundations for a nonlinear theory of distributional geometry that is developed in a subsequent paper that is based on Colombeau algebras of tensor distributions on manifolds.

Authors

I am an author on this paper
Click your name to claim this paper and add it to your profile.

Reviews

Primary Rating

4.5
Not enough ratings

Secondary Ratings

Novelty
-
Significance
-
Scientific rigor
-
Rate this paper

Recommended

No Data Available
No Data Available