Blow-up of regular submanifolds in Heisenberg groups and applications
Classical Analysis and ODEs
2007-05-23 v1 Differential Geometry
Abstract
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.
Cite
@article{arxiv.math/0506445,
title = {Blow-up of regular submanifolds in Heisenberg groups and applications},
author = {Valentino Magnani},
journal= {arXiv preprint arXiv:math/0506445},
year = {2007}
}