Sub-Riemannian Calculus on Hypersurfaces in Carnot Groups
D. Danielli, N. Garofalo, D.M. Nhieu
TL;DR
This paper develops fundamental geometric tools and properties for hypersurfaces within Carnot groups, advancing the understanding of sub-Riemannian geometry in these complex structures.
Contribution
It introduces new geometric quantities and properties specific to hypersurfaces in Carnot groups, filling a gap in sub-Riemannian geometric analysis.
Findings
Defined basic geometric quantities for hypersurfaces in Carnot groups
Established properties of these hypersurfaces in the sub-Riemannian context
Provided foundational tools for further geometric analysis in Carnot groups
Abstract
We develope basic geometric quantities and properties of hypersurfaces in Carnot groups.
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Taxonomy
TopicsGeometric Analysis and Curvature Flows · Advanced Differential Geometry Research · Algebraic and Geometric Analysis