Stability of Heisenberg Isoperimetric Profiles
Francescopaolo Montefalcone
TL;DR
This paper investigates the stability properties of isoperimetric profiles, which are constant mean curvature hypersurfaces in Heisenberg groups, aiming to understand their geometric and variational stability in sub-Riemannian geometry.
Contribution
It provides a detailed analysis of the stability of isoperimetric profiles in Heisenberg groups, a topic not extensively explored before.
Findings
Characterization of isoperimetric profiles in Heisenberg groups
Results on stability conditions for these profiles
Insights into geometric variational properties
Abstract
In the context of sub-Riemannian Heisenberg groups Hn, n \geq 1, we shall study Isoperimetric Profiles, which are closed compact hypersurfaces having constant horizontal mean curvature, very similar to ellipsoids. Our main goal is to study the stability of Isoperimetric Profiles.
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Taxonomy
TopicsGeometric Analysis and Curvature Flows · Geometry and complex manifolds · Advanced Differential Geometry Research