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Submanifolds in Carnot Groups by Davide Vittone

Submanifolds in Carnot Groups

by Davide Vittone
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Book cover type: Paperback
  • ISBN13: 9788876423277
  • Binding: Paperback
  • Subject: N/A
  • Publisher: Edizioni Della Normale
  • Publisher Imprint: Edizioni Della Normale
  • Publication Date:
  • Pages: 180
  • Original Price: USD 29.95
  • Language: English
  • Edition: 2008
  • Item Weight: 409 grams
  • BISAC Subject(s): Geometry / Differential

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.

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