Theses (Scuola Normale Superiore)
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Submanifolds in Carnot Groups

Authors: Vittone, Davide

  • Characterizes intrinsically regular hypersurfaces in Heisenberg groups in terms of a suitable notion of graphs, the so-called X-graphs
  • Solves the Bernstein problem for regular X-graphs in the first Heisenberg group, and classifies solutions
  • Computes the Hausdorff measure of submanifolds with arbitrary codimension under a genericity assumption, in the setting of Carnot groups
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About this book

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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Softcover 18,72 €
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Bibliographic Information

Bibliographic Information
Book Title
Submanifolds in Carnot Groups
Authors
Series Title
Theses (Scuola Normale Superiore)
Series Volume
7
Copyright
2008
Publisher
Edizioni della Normale
Copyright Holder
Edizioni della Normale
Softcover ISBN
978-88-7642-327-7
Series ISSN
2239-1460
Edition Number
1
Number of Pages
XX, 180
Topics