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A Blow-up Theorem for regular hypersurfaces on nilpotent groups by Valentino Magnani is a nonfiction available to read on EtoBox.

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We obtain an intrinsic Blow-up Theorem for regular hypersurfaces on graded nilpotent groups. This procedure allows us to represent explicitly the Riemannian surface measure in terms of the spherical Hausdorff measure with respect to an intrinsic distance of the group, namely homogeneous distance. We apply this result to get a version of the Riemannian coarea forumula on sub-Riemannian groups, that can be expressed in terms of arbitrary homogeneous distances.We introduce the natural class of horizontal isometries in sub-Riemannian groups, giving examples of rotational invariant homogeneous distances and rotational groups, where the coarea formula takes a simpler form. By means of the same Blow-up Theorem we obtain an optimal estimate for the Hausdorff dimension of the characteristic set relative to C1,1 hypersurfaces in 2-step groups and we prove that it has finite Q − 2 Hausdorff measure, where Q is the homogeneous dimension of the group.

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Author

Valentino Magnani

Publisher

Springer; Springer-Verlag; Springer Verlag; Springer Science and Business Media LLC; Society for Mining, Metallurgy and Exploration Inc. (ISSN 0025-2611)

Published

2003

Language

EN

Category

nonfiction

Subjects

Mathematics, Stem