This article analyzes minimal length connections among three points in a geometric space, suggesting improved understanding of sub-Riemannian geometry.
Key Points
The aim is to find and characterize minimal horizontal triods connecting three points in the Heisenberg group.
Proved the existence of minimal horizontal triods.
Characterized these triods for further analysis.
Formulated a horizontal curve shortening flow to deform initial triods into critical points.
Conducted numerical experiments using a fully discrete finite element scheme.
Identified various forms of minimal horizontal triods.
Established the effectiveness of the curve shortening flow.
Demonstrated rich geometrical insights through numerical experiments.