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Growth of a primitive of a differential form

Jean-Claude Sikorav (2001)

Bulletin de la Société Mathématique de France

For an exact differential form on a Riemannian manifold to have a primitive bounded by a given function f , by Stokes it has to satisfy some weighted isoperimetric inequality. We show the converse up to some constants if M has bounded geometry. For a volume form, it suffices to have the inequality ( | Ω | Ω f d σ for every compact domain Ω M ). This implies in particular the “well-known” result that if M is the universal covering of a compact Riemannian manifold with non-amenable fundamental group, then the volume...

Local density of diffeomorphisms with large centralizers

Christian Bonatti, Sylvain Crovisier, Gioia M. Vago, Amie Wilkinson (2008)

Annales scientifiques de l'École Normale Supérieure

Given any compact manifold M , we construct a non-empty open subset 𝒪 of the space Diff 1 ( M ) of C 1 -diffeomorphisms and a dense subset 𝒟 𝒪 such that the centralizer of every diffeomorphism in 𝒟 is uncountable, hence non-trivial.

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