Submanifolds in Carnot groups by Davide VittoneSubmanifolds in Carnot groups by Davide Vittone

Submanifolds in Carnot groups

byDavide Vittone

Paperback | May 16, 2008

Pricing and Purchase Info

$37.35 online 
$41.50 list price save 10%
Earn 187 plum® points

Prices and offers may vary in store


In stock online

Ships free on orders over $25

Not available in stores


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 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.

Title:Submanifolds in Carnot groupsFormat:PaperbackDimensions:180 pagesPublished:May 16, 2008Publisher:Springer-Verlag/Sci-Tech/TradeLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:8876423273

ISBN - 13:9788876423277


Table of Contents

Preface.- 1. Carnot groups.- 2. Measure of submanifolds on Carnot groups.- 3. Elements of Geometric Measure Theory in the Heisenberg group.- 4. Intrinsic parametrization of H-regular surfaces.- 5. The Bernstein problem in Heisenberg groups and calibrations.