Diffeomorphism groups of compact convex sets

2016/03/18 by Helge Glockner, Glockner, Helge, Karl-Hermann Neeb +1
Mathematics · #22E65 (primary) #34A12 (secondary) #FOS: Mathematics #Group Theory (math.GR) #math.GR #msc:22E65 #msc:34A12

paper · pdf · doi:10.48550/arxiv.1603.05995

33 pages, LaTeX

arxiv created 2016/03/18 · arxiv updated 2016/03/22

Abstract

For a compact convex subset K with non-empty interior in a finite-dimensional vector space, let G be the group of all smooth diffeomorphisms of K which fix the boundary of K pointwise. We show that G is a C⁰-regular infinite-dimensional Lie group. As a byproduct, we obtain results concerning solutions to ordinary differential equations on compact convex sets.

Related

• Diffeomorphism groups of convex polytopes
• Infinite-Dimensional Lie Groups
• Direct limits of regular Lie groups
• Boundary values of diffeomorphisms of simple polytopes, and controllability
• Diffeomorphism groups of critical regularity