Sub-Riemannian calculus and monotonicity of the perimeter for graphical strips
We prove a monotonicity result at specific points for the Horizontal Perimeter for a class of surfaces in the Heisenberg group.
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arXiv subjects
D. Danielli
Publications and source records attributed to D. Danielli.
A partial solution of the isoperimetric problem for the Heisenberg group
We provide a partial solution to the isoperimetric problem in the Heisenberg group.
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A notable family of entire intrinsic minimal graphs in the Heisenberg group which are not perimeter minimizing
We prove that a family of entire intrinsic minimal graphs in the Heisenberg group are not perimeter minimizing.
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Instability of graphical strips and a positive answer to the Bernstein problem in the Heisenberg group
Let S be a C^2 H-minimal noncharacteristic hypersurface in the first Heisenberg group. We show that if S contains a graphical strip, then it is not a stable minimal surface. Moreover, we show that if S is a C^2 H-minimal noncharacteristic entire graph which is not itself a vertical plane, then S contains a graphical strip. Thus, as a corollary, we obtain an analogue of the Bernstein theorem: the only stable C^2 H-minimal noncharacteristic entire graphs are the vertical planes.
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Sub-Riemannian Calculus on Hypersurfaces in Carnot Groups
We develope basic geometric quantities and properties of hypersurfaces in Carnot groups.
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