A general approach to compute the spherical measure of submanifolds in homogeneous groups is provided. We focus our attention on the homogeneous tangent space, that is a suitable weighted algebraic expansion of the submanifold. This space plays a central role for the existence of blow-ups. Main applications are area-type formulae for new classes of C1 smooth submanifolds and the equality between spherical measure and Hausdorff measure on all horizontal submanifolds.
Towards a theory of area in homogeneous groups
Magnani, Valentino
2019-01-01
Abstract
A general approach to compute the spherical measure of submanifolds in homogeneous groups is provided. We focus our attention on the homogeneous tangent space, that is a suitable weighted algebraic expansion of the submanifold. This space plays a central role for the existence of blow-ups. Main applications are area-type formulae for new classes of C1 smooth submanifolds and the equality between spherical measure and Hausdorff measure on all horizontal submanifolds.File in questo prodotto:
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