L¹-Poincaré inequalities for differential forms on Euclidean spaces and Heisenberg groups

2019/02/13 by Baldi, Annalisa, Franchi, Bruno, Pansu, Pierre
#Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1902.04819

Abstract

In this paper, we prove interior Poincaré and Sobolev inequalities in Euclidean spaces and in Heisenberg groups, in the limiting case where the exterior (resp. Rumin) differential of a differential form is measured in L 1 norm. Unlike for L p , p > 1, the estimates are doomed to fail in top degree. The singular integral estimates are replaced with inequalities which go back to Bourgain-Brezis in Euclidean spaces, and to Chanillo-van Schaftingen in Heisenberg groups.

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