A partial solution of the isoperimetric problem for the Heisenberg group
N. Garofalo, D. Danielli, D.M. Nhieu
TL;DR
This paper addresses the isoperimetric problem within the Heisenberg group, offering partial insights into the shape and properties of optimal solutions in this non-Euclidean setting.
Contribution
It presents a partial solution to the isoperimetric problem specifically tailored for the Heisenberg group, advancing understanding in sub-Riemannian geometry.
Findings
Identifies specific conditions for isoperimetric sets in the Heisenberg group
Provides partial characterization of optimal shapes
Suggests directions for complete solutions
Abstract
We provide a partial solution to the isoperimetric problem in the Heisenberg group.
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Taxonomy
TopicsGeometric Analysis and Curvature Flows · advanced mathematical theories · Spectral Theory in Mathematical Physics