English

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}
}