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.

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Titolo Submanifolds in Carnot Groups
Autore Davide Vittone
Editing/translation No
ISBN 978-88-7642-327-7
Anno di pubblicazione 2008
Oggetto No
Link acquista
Notes No