Growth of a primitive of a differential form
摘要
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 (|| f d for every compact domain 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 form has a bounded primitive. Thanks to a recent theorem of A. uk, we also obtain that if the fundamental group is infinite, the volume form always has a primitive with linear growth.
引用本文（GB/T 7714）
Jean-Claude Sikorav. Growth of a primitive of a differential form[J]. Bulletin de la Société mathématique de France, 2001.
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