We obtain a blow-up theorem for regular submanifolds in the Heisenberg group, where intrinsic dilations are used. Main consequence of this result is an explicit formula for the density of (p+1)-dimensional spherical Hausdorff measure restricted to a p-dimensional submanifold with respect to the Riemannian surface measure. We explicitly compute this formula in some simple examples and we present a lower semicontinuity result for the spherical Hausdorff measure with respect to the weak convergence of currents. Another application is the proof of an intrinsic coarea formula for vector-valued mappings on the Heisenberg group.
@article{bwmeta1.element.doi-10_1007_s11533-005-0006-1,
author = {Valentino Magnani},
title = {Blow-up of regular submanifolds in Heisenberg groups and applications},
journal = {Open Mathematics},
volume = {4},
year = {2006},
pages = {82-109},
zbl = {1097.53020},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_1007_s11533-005-0006-1}
}
Valentino Magnani. Blow-up of regular submanifolds in Heisenberg groups and applications. Open Mathematics, Tome 4 (2006) pp. 82-109. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_1007_s11533-005-0006-1/
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