Weighted diffeomorphism groups of Riemannian manifolds
Differential Geometry
2016-01-13 v1 Functional Analysis
Abstract
In this paper, we define locally convex vector spaces of weighted vector fields and use them as model spaces for Lie groups of weighted diffeomorphisms on Riemannian manifolds. We prove an easy condition on the weights that ensures that these groups contain the compactly supported diffeomorphisms. We finally show that for the special case where the manifold is the euclidean space, these Lie groups coincide with the ones constructed in the author's earlier work ["Weighted diffeomorphism groups of Banach spaces and weighted mapping groups". In: Dissertationes Math. 484 (2012), p. 128. DOI: 10.4064/dm484-0-1].
Keywords
Cite
@article{arxiv.1601.02834,
title = {Weighted diffeomorphism groups of Riemannian manifolds},
author = {Boris Walter},
journal= {arXiv preprint arXiv:1601.02834},
year = {2016}
}