Submanifolds in Carnot Groups

This book is devoted to the study of submanifolds in the setting of Carnot groups equipped with a sub-Riemannian structure. It places particular emphasis on the case of Heisenberg groups.

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

Contenu

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.