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 leadingto the analysis of Plateau and Bernstein type problems. Intrinsically regularhypersurfaces 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 TheHausdorff measure of submanifolds with arbitrary codimension is computed, under a genericity assumption, in the setting of Carnot groups INDICE: 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.
- ISBN: 978-88-7642-327-7
- Editorial: Springer
- Encuadernacion: Rústica
- Páginas: 200
- Fecha Publicación: 01/05/2008
- Nº Volúmenes: 1
- Idioma: Inglés