Submanifolds in Carnot Groups Zoom

Davide Vittone

Submanifolds in Carnot Groups

pp. xx-178

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The book is devoted to the study of submanifolds in the setting of Carnot groups equipped with a sub-Riemannian structure; particular emphasis is given to the case of Heisenberg groups. A Geometric Measure Theory viewpoint is adopted, and features such as intrinsic perimeters, Hausdorff measures, area formulae, calibrations and minimal surfaces are considered. Area formulae for the measure of submanifolds of arbitrary codimension are obtained in Carnot groups. Intrinsically regular hypersurfaces in the Heisenberg group are extensively studied: suitable notions of graphs are introduced, together with area formulae leading to the analysis of Plateau and Bernstein type problems.

Additional Information

Additional Information

Title Submanifolds in Carnot Groups
Author (display) Davide Vittone
Editing/translations No
ISBN 978-88-7642-327-7
Publishing year 2008
Subject No
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Notes No