Family of Riemannian problems on the Heisenberg group
Yu. Sachkov
TL;DR
This paper investigates a series of Riemannian problems on the Heisenberg group, which gradually approximate the sub-Riemannian problem, providing insights into their geometric and analytical properties.
Contribution
It introduces a family of Riemannian problems on the Heisenberg group that converge to the sub-Riemannian problem, bridging the gap between Riemannian and sub-Riemannian geometries.
Findings
Analysis of the limiting behavior of Riemannian problems
Characterization of geometric properties approaching sub-Riemannian case
Potential applications to control theory and geometric analysis
Abstract
We study a family of Riemannian problems on the Heisenberg group that tends to the sub-Riemannian problem on this group.
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Taxonomy
TopicsGeometric Analysis and Curvature Flows · Nonlinear Partial Differential Equations · Numerical methods in inverse problems