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- W2949233633 abstract "We study the class of transversal submanifolds. We characterize their blow-ups at transversal points and prove a negligibility theorem for their generalized characteristic set, with respect to the Carnot-Carath'eodory Hausdorff measure. This set is made by all points of non-maximal degree. Observing that C^1 submanifolds in Carnot groups are generically transversal, the previous results prove that the intrinsic of C^1 submanifolds is generically equivalent to their Carnot-Carath'eodory Hausdorff measure. As a result, the restriction of this Hausdorff measure to the submanifold can be replaced by a more manageable integral formula, that should be seen as a sub-Riemannian mass. Another consequence of these results is an explicit formula, only depending on the embedding of the submanifold, that computes the Carnot-Carath'eodory Hausdorff dimension of C^1 transversal submanifolds." @default.
- W2949233633 created "2019-06-27" @default.
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- W2949233633 date "2012-11-28" @default.
- W2949233633 modified "2023-09-27" @default.
- W2949233633 title "On transversal submanifolds and their measure" @default.
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