Submanifolds with boundary in sub-Riemannian Heisenberg Groups

2025/08/21 by Di Marco, Marco, Vittone, Davide
#26B20 #53C17 #53C65 #58C35 #Classical Analysis and ODEs (math.CA) #Differential Geometry (math.DG) #FOS: Mathematics #Metric Geometry (math.MG)

paper · doi:10.48550/arxiv.2508.15634

Abstract

We discuss the notion of submanifolds with boundary with intrinsic C¹ regularity in sub-Riemannian Heisenberg groups and we provide some examples. Eventually, we present a Stokes' Theorem for such submanifolds involving the integration of Rumin's differential forms in Heisenberg groups.

Citations

• Submanifolds with boundary and Stokes' Theorem in Heisenberg groups
• Area of intrinsic graphs in homogeneous groups
• Flat compactness of normal currents, and charges in Carnot groups
• An alternative construction of the Rumin complex on homogeneous nilpotent Lie groups
• Sobolev mappings and the spectral sequence for Rumin's filtration on the de Rham complex
• Sobolev mappings and the Rumin complex
• Pansu pullback and rigidity of mappings between Carnot groups
• Area formula for regular submanifolds of low codimension in Heisenberg groups

Related

• Submanifolds with boundary and Stokes' Theorem in Heisenberg groups
• Intrinsic Regular Surfaces of low codimension in Heisenberg groups
• Intersections of intrinsic submanifolds in the Heisenberg group
• Curvature estimates for minimal hypersurfaces in the Heisenberg group
• Area-stationary and stable surfaces of class C¹ in the sub-Riemannian\n Heisenberg group mathbb H¹