Revista Matemática Iberoamericana

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Volume 26, Issue 1, 2010, pp. 333–346
DOI: 10.4171/RMI/603

Published online: 2010-04-30

Measure of submanifolds in the Engel group

Enrico Le Donne[1] and Valentino Magnani[2]

(1) University of Jyväskylä, Finland
(2) Università di Pisa, Italy

We find all intrinsic measures of $C^{1,1}$ smooth submanifolds in the Engel group, showing that they are equivalent to the corresponding $d$-dimensional spherical Hausdorff measure restricted to the submanifold. The integer $d$ is the degree of the submanifold. These results follow from a different approach to negligibility, based on a blow-up technique.

Keywords: Engel group, submanifolds, Hausdorff measure

Le Donne Enrico, Magnani Valentino: Measure of submanifolds in the Engel group. Rev. Mat. Iberoam. 26 (2010), 333-346. doi: 10.4171/RMI/603