Variation of Perimeter Measure in sub-Riemannian geometry

Abstract

We derive a formula for the first variation of horizontal perimeter measure for $C^2$ hypersurfaces of completely general sub-Riemannian manifolds, allowing for the existence of characteristic points. For $C^2$ hypersurfaces in vertically rigid sub-Riemannian manifolds we also produce a second variation formula for variations supported away from the characteristic locus. This variation formula is used to show the bubble sets in \hn{2} are stable under volume preserving variations.

37 pages

References in corpus (4)

• Exterior Differential Systems and Euler-Lagrange Partial Differential Equations
• The Bernstein Problem in the Heisenberg Group
• Rotationally invariant hypersurfaces with constant mean curvature in the Heisenberg group H^n
• Instability of graphical strips and a positive answer to the Bernstein problem in the Heisenberg group

Cited by in corpus (1)

• Isoperimetric, Sobolev and Poincaré inequalities on hypersurfaces in sub-Riemannian Carnot groups