Submanifolds in Carnot Groups

ISBN-13: 9788876423277 / Angielski / Miękka / 2008 / 180 str.

Davide Vittone

Opis

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.

Spis treści

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.