Revista Matemática Iberoamericana

Measure of submanifolds in the Engel group

Enrico Le Donne and Valentino Magnani

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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.

Article information

Rev. Mat. Iberoamericana, Volume 26, Number 1 (2010), 333-346.

First available in Project Euclid: 16 February 2010

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 58C35: Integration on manifolds; measures on manifolds [See also 28Cxx]
Secondary: 22E25: Nilpotent and solvable Lie groups 53C17: Sub-Riemannian geometry

Engel group submanifolds Hausdorff measure


Le Donne, Enrico; Magnani, Valentino. Measure of submanifolds in the Engel group. Rev. Mat. Iberoamericana 26 (2010), no. 1, 333--346.

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