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- W1736866498 abstract "We investigate metric properties of level sets of horizontally differentiable maps defined on the first Heisenberg group $(Bbb{H}^1,d_{cc})$ equipped with the standard sub-Riemannian structure. In particular, we present an exhaustive analysis in a new case of a map $Fin C^1_H(Bbb{H}^1, Bbb{R}^2)$ with surjective horizontal differential (an analogue of the classical implicit function theorem). Among other results, we show that a level set of such map is locally a simple curve of Hausdorff sub-Riemannian dimension 2, but, surprisingly, in general its two-dimensional Hausdorff measure can be zero or infinity. Therefore, those level sets (called textsf{vertical curves}) can be of rough nature and not belong to the class of intrinsic regular manifolds." @default.
- W1736866498 created "2016-06-24" @default.
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- W1736866498 date "2011-10-17" @default.
- W1736866498 modified "2023-09-27" @default.
- W1736866498 title "Roughness of level sets of differentiable maps on Heisenberg group" @default.
- W1736866498 hasPublicationYear "2011" @default.
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