Overview
- Intrinsically regular hypersurfaces in Heisenberg groups are characterized in terms of a suitable notion of graphs, the so-called X-graphs
- The Bernstein problem for regular X-graphs is solved in the first Heisenberg group, and solutions are classified
- The Hausdorff measure of submanifolds with arbitrary codimension is computed, under a genericity assumption, in the setting of Carnot groups
Part of the book series: Publications of the Scuola Normale Superiore (PSNS, volume 7)
Part of the book sub series: Theses (Scuola Normale Superiore) (TSNS)
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Keywords
- Bernstein problem
- Carnot group
- Hausdorff measure
- Heisenberg group
- geometric measure theory
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.
Authors and Affiliations
Bibliographic Information
Book Title: Submanifolds in Carnot Groups
Authors: Davide Vittone
Series Title: Publications of the Scuola Normale Superiore
Publisher: Edizioni della Normale Pisa
Copyright Information: Edizioni della Normale 2008
Softcover ISBN: 978-88-7642-327-7Due: 16 May 2008
Series ISSN: 2239-1460
Series E-ISSN: 2532-1668
Edition Number: 1
Number of Pages: XX, 180