Abstract
We study the arithmetic three-spheres theorems for subsolutions of subelliptic PDEs of p p -harmonic type in Carnot groups of Heisenberg type for 1 > p > â 1>p>\infty . In the presentation we exhibit the special cases of sub-Laplace equations ( p = 2 p=2 ) and the case p p is equal to the homogeneous dimension of a Carnot group. Corollaries include asymptotic behavior of subsolutions for small and large radii and the Liouville-type theorems.
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