Stable H-minimal hypersurfaces
Francescopaolo Montefalcone
TL;DR
This paper investigates the stability properties of smooth H-minimal hypersurfaces within sub-Riemannian Carnot groups, utilizing variation formulas for the H-perimeter measure to establish new stability results.
Contribution
It provides new stability results for H-minimal hypersurfaces in Carnot groups using first and second variation formulas.
Findings
Established stability criteria for H-minimal hypersurfaces
Derived formulas for the first and second variation of H-perimeter
Extended stability analysis to sub-Riemannian k-step Carnot groups
Abstract
We prove some stability results for smooth H-minimal hypersurfaces immersed in a sub-Riemannian k-step Carnot group G. The main tools are the formulas for the 1st and 2nd variation of the H-perimeter measure.
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Taxonomy
TopicsGeometric Analysis and Curvature Flows · Geometry and complex manifolds · Dermatological and Skeletal Disorders