Non-horizontal submanifolds and coarea formula
From MaRDI portal
Publication:1001387
DOI10.1007/s11854-008-0045-1zbMath1158.22006OpenAlexW2002983652MaRDI QIDQ1001387
Publication date: 17 February 2009
Published in: Journal d'Analyse Mathématique (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/s11854-008-0045-1
Nilpotent and solvable Lie groups (22E25) Global submanifolds (53C40) Sub-Riemannian geometry (53C17)
Related Items
Area of intrinsic graphs and coarea formula in Carnot groups, Rank-one theorem and subgraphs of BV functions in Carnot groups, A reverse coarea-type inequality in Carnot groups, Marstrand's density theorem in the Heisenberg group, A coarea formula for smooth contact mappings of Carnot-Carathéodory spaces, Measure of curves in graded groups, Towards a theory of area in homogeneous groups, A primer on Carnot groups: homogenous groups, Carnot-Carathéodory spaces, and regularity of their isometries, Area formula for regular submanifolds of low codimension in Heisenberg groups, A low rank property and nonexistence of higher-dimensional horizontal Sobolev sets, Measure of submanifolds in the Engel group, Blow-up estimates at horizontal points and applications, Removable sets for Lipschitz harmonic functions on Carnot groups, On transversal submanifolds and their measure, Rotational symmetries and spherical measure in homogeneous groups
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Characteristic points, rectifiability and perimeter measure on stratified groups
- Regular submanifolds, graphs and area formula in Heisenberg groups
- Sub-Riemannian vs. Euclidean dimension comparison and fractal geometry on Carnot groups
- Blow-up estimates at horizontal points and applications
- Instability of graphical strips and a positive answer to the Bernstein problem in the Heisenberg group \(\mathbb H^1\)
- Sobolev and isoperimetric inequalities for degenerate metrics
- On the structure of finite perimeter sets in step 2 Carnot groups
- Note on coarea formulae in the Heisenberg group
- A blow-up theorem for regular hypersurfaces on nilpotent groups
- The geometric Sobolev embedding for vector fields and the isoperimetric inequality
- Rectifiability of sets of finite perimeter in Carnot groups: existence of a tangent hyperplane
- Sub-Riemannian calculus on hypersurfaces in Carnot groups
- Regular hypersurfaces, intrinsic perimeter and implicit function theorem in Carnot groups
- Stability of isometric maps in the Heisenberg group
- Ahlfors type estimates for perimeter measures in Carnot-Carathéodory spaces
- Blow-up of regular submanifolds in Heisenberg groups and applications
- The Bernstein problem for intrinsic graphs in Heisenberg groups and calibrations
- Measures with unique tangent measures in metric groups
- Convex isoperimetric sets in the Heisenberg group
- A notable family of entire intrinsic minimal graphs in the Heisenberg group which are not perimeter minimizing
- An intrinsic measure for submanifolds in stratified groups
- Regular domains in homogeneous groups
- Hardy Spaces on Homogeneous Groups. (MN-28), Volume 28
- Lifts of Lipschitz maps and horizontal fractals in the Heisenberg group
- The coarea formula for real‐valued Lipschitz maps on stratified groups
- Rectifiability and perimeter in the Heisenberg group
