Weighted diffeomorphism groups of Riemannian manifolds

2016/01/12 by Boris Walter, Walter, Boris
Mathematics · #46T05 #46T10 #58B25 #58C25 #Differential Geometry (math.DG) #FOS: Mathematics #Functional Analysis (math.FA) #Primary 58D05 #Secondary 22E65 #math.DG #math.FA #msc:22E65 #msc:46T05 #msc:46T10 #msc:58B25 #msc:58C25 #msc:58D05

paper · pdf · doi:10.48550/arxiv.1601.02834

arxiv created 2016/01/12 · arxiv updated 2016/01/13

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].

Citations

• Weighted diffeomorphism groups of Banach spaces and weighted mapping groups

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