Revista Matemática Iberoamericana

Measure of submanifolds in the Engel group

Enrico Le Donne and Valentino Magnani

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Abstract

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

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

Dates
First available in Project Euclid: 16 February 2010

Permanent link to this document
https://projecteuclid.org/euclid.rmi/1266330126

Mathematical Reviews number (MathSciNet)
MR2666317

Zentralblatt MATH identifier
1198.58007

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

Keywords
Engel group submanifolds Hausdorff measure

Citation

Le Donne, Enrico; Magnani, Valentino. Measure of submanifolds in the Engel group. Rev. Mat. Iberoamericana 26 (2010), no. 1, 333--346. https://projecteuclid.org/euclid.rmi/1266330126


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References

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