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Mathematics > Metric Geometry

arXiv:1810.08094 (math)
[Submitted on 18 Oct 2018]

Title:Towards a theory of area in homogeneous groups

Authors:Valentino Magnani
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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 $C^1$ smooth submanifolds. We also study various classes of distances, showing how their symmetries lead to simpler area and coarea formulas. Finally, we establish the equality between spherical measure and Hausdorff measure on all horizontal submanifolds.
Comments: 60 pages
Subjects: Metric Geometry (math.MG)
Cite as: arXiv:1810.08094 [math.MG]
  (or arXiv:1810.08094v1 [math.MG] for this version)
  https://doi.org/10.48550/arXiv.1810.08094

Submission history

From: Valentino Magnani [view email]
[v1] Thu, 18 Oct 2018 14:59:24 UTC (51 KB)
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