Continuous primitives for higher degree differential forms in Euclidean spaces, Heisenberg groups and applications

2024/03/25 by Baldi, Annalisa, Franchi, Bruno, Pansu, Pierre
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2403.16602

Abstract

It is shown that higher degree exact differential forms on compact Riemannian n-manifolds possess continuous primitives whose uniform norm is controlled by their Lⁿ norm. A contact sub-Riemannian analogue is proven, with differential forms replaced with Rumin differential forms.

Related

• Cohomology of annuli, duality and L^∞-differential forms on Heisenberg groups
• Diffeological Smoothness in Hodge Theory
• Bounds on primitives of differential forms and cofilling inequalities
• On Poincaré lemma or Volterra theorem about differential forms and cohomology groups
• Diffeologies, Differential Spaces, and Symplectic Geometry