Multiexponential maps in Carnot groups with applications to convexity and differentiability

DOI10.1007/s10231-020-00994-3zbMath1478.53061arXiv1908.01124OpenAlexW3037812856MaRDI QIDQ2662179

Daniele Morbidelli, Annamaria Montanari

Publication date: 9 April 2021

Published in: Annali di Matematica Pura ed Applicata. Serie Quarta (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1908.01124

zbMATH Keywords

cone propertyCarnot groupsPansu differentiabilitysub-Riemannian distancehorizontal convexity

Mathematics Subject Classification ID

Existence theories for optimal control problems involving ordinary differential equations (49J15) Sub-Riemannian geometry (53C17)

Related Items

Monotone sets and local minimizers for the perimeter in Carnot groups ⋮ Horizontally quasiconvex envelope in the Heisenberg group ⋮ Precisely monotone sets in step-2 rank-3 Carnot algebras

Cites Work

• Regularity of sets with constant horizontal normal in the Engel group
• Metric differentiation, monotonicity and maps to \(L^{1}\)
• Differentiability of intrinsic Lipschitz functions within Heisenberg groups
• Sets with finite \(\mathbb{H}\)-perimeter and controlled normal
• Regularity properties of \(H\)-convex sets
• On the lack of semiconcavity of the subRiemannian distance in a class of Carnot groups
• Carnot-Carathéodory metrics and quasiisometries of symmetric spaces of rank 1
• Hypoellipticite analytique sur des groupes nilpotents de rang 2
• Rigidity of integral curves of rank 2 distributions
• On the structure of finite perimeter sets in step 2 Carnot groups
• Universal differentiability sets and maximal directional derivatives in Carnot groups
• Sub-Finsler geodesics on the Cartan group
• Structure of porous sets in Carnot groups
• On the inner cone property for convex sets in two-step Carnot groups, with applications to monotone sets
• Intrinsic Lipschitz graphs within Carnot groups
• The Bernstein problem for intrinsic graphs in Heisenberg groups and calibrations
• Stratified Lie Groups and Potential Theory for their Sub-Laplacians
• Exponential map in the generalized Dido problem
• Shortest paths for sub-Riemannian metrics on rank-two distributions
• A Comprehensive Introduction to Sub-Riemannian Geometry
• Cohomologie des algèbres de Lie nilpotentes. Application à l'étude de la variété des algèbres de Lie nilpotentes