Poincaré and Sobolev inequalities for differential forms in Heisenberg groups

2017/11/27 by Annalisa Baldi, Baldi, Annalisa, Bruno Franchi +3 · 1 citation
Engineering · Mathematics · #Advanced Numerical Analysis Techniques #Differential Geometry (math.DG) #FOS: Mathematics #Functional Analysis (math.FA) #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology

paper · pdf · doi:10.48550/arxiv.1711.09786

openalex publication_date 2017/11/27 · openalex created_date 2017/12/04 · openalex updated_date 2026/07/28

Abstract

Poincaré and Sobolev inequalities for differential forms on Heisenberg balls, involving Rumin's differentials, are given. Furthermore, a global homotopy of Rumin's complex which improves differentiability of Rumin forms is provided on any bounded geometry contact manifold.

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• Averages and the ℓ^q,1-cohomology of Heisenberg groups

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